Chapter 2: Financial Markets: Part 2



Chapter 2: Financial Markets: Part 2

Portfolio Allocation and the demand for assets

There are three main determinants of asset pricing:

1) Expected return: The higher the expected return of the asset, all else constant, the higher the price of the asset. Naturally, we will discuss at length the factors that influence the expected return of the asset(s) throughout the course. I do want to mention at this point how important expectations and changes in expectations are in terms of determining not only asset prices, but also, aggregate economic activity.

Asset price = f (Rete) :

+

{stated as “the asset price is a positive (+) function (f) of it’s expected return (Rete), all else constant}

2) Liquidity: Liquidity is an attractive quality in any asset and a highly liquid asset has three qualities: 1) it is easy (low cost) to convert the asset into money where money is defined as transactions money; 2) it can be converted to money quickly and 3) the amount that it is converted to is representative of its fundamental value (i.e., I can sell my house very quickly and easily for $5, but that doesn’t mean it is liquid!). Typically, the more liquid the asset, the lower the return. Take money, typically considered to be the most liquid asset of all. Money earns a nominal return of zero and a real return equal to the ‘negative’ of the inflation rate.[1]

Liquidity is especially attractive in a highly uncertain environment. When we discuss financial crises and shocks like 9/11, we will see the impact on financial markets when investors demand more liquid assets. US Treasuries are often considered very liquid and thus the term: “rush to the safe haven of US Treasuries.” The safe haven refers naturally to the perceived zero default risk quality of US Treasuries.

Asset price = f (Liq) :

+

{stated as “the asset price is a positive (+) function (f) of it’s liquidity (Liq), all else constant}

3) Risk: The more risky the asset, the more uncertain as to the assets’ return. Risk arises for a variety of reasons and we assume that all else equal, investors prefer assets with less risk (i.e., on average, investors are risk averse). We also note that risk and expected return are related – typically, the higher the risk, the higher the expected return (investors require a higher expected return to take on the higher risk).

Asset price = f (Risk) :

-

{stated as “the asset price is a negative (-) function (f) of it’s Risk, all else constant}

Stock Price Determination

As most of us could gather, the obvious driving force underlying any the price of any stock is the expected future stream of profits or earnings (earnings and profits are used interchangeably). We need to be more specific, it is the present value (PV) of current and future earnings that matter. We all should recall that the present value of say $1,000 today is larger than the present value of $1,000 ten years from now. But how much larger? The answer depends on the expected nominal interest rate to prevail over the next ten years. Let’s make life simple, let us suppose that the interest rate over the next ten years will be 10% year in and year out. In this case, given these assumptions, the PV of $1,000 ten years from now would be:

PV1000 = $1,000/(1 + 0.10)10 = $ 385.54

What does $385.54 represent? The answer is that if we take $385.54 and invest it today at a 10% annual return and take the principal and interest and continue rolling it over for 10 years, at the end of the 10th year, we would have $1,000. An equivalent way of thinking about this is, and the way most relevant for understanding how stock prices are determined is the following: Given the above conditions, I would be willing to pay $385.54 today, to receive $1,000 ten years from now. In what follows, the $1,000 in this example would be the “expected profits” of the firm ten years from now. These expected profits are continuously changing given the continuous NEWS that investors digest and process on a day to day basis.

In terms of stock price determination, investors form expectations as to the future profits of any particular firm as well as the expected path of interest rates, since together, they determine the present value of the firm. Similar to the above, the present value of a firm can be thought of as the most investors would be willing to pay for the firm today, to have the ownership rights to all the current and future profits expected in the future. When we divide the present value of the firm by the number of shares of stock outstanding, we arrive at the price of the stock. Before getting into more specifics, please read the following summation.

Three major factors to keep in mind when considering stock price determination

1) Stock prices are driven by expectations and changes in expectations. Just about everything influences expectations and these changes in expectations are reflected immediately in the relevant stock price.[2]

2) Stock prices are positively related to expected earnings and expected earnings nearer to the present have a stronger influence on stock prices than do the same expected earnings further out into the future. For example, the present value of $10,000 in expected earnings 2 years from now is larger than the present value of $10,000 in expected earnings 10 years from now (assuming away zero interest rates)[3]

3) Stock Prices are typically negatively related to the expected path of interest rates. The expected path of interest rates is so important in financial markets, not to mention, aggregate economic activity. Many investors spend much of their time trying to figure out what the Federal Reserve may or may not do. Interest rates also change for reasons not directly related to Fed policy, and a big portion of this class revolves around interest rate determination. For the present, we need to understand why lower interest rates are ‘typically’ good for stocks. First, the present value of future profits rises the lower the expected path of interest rates. Let’s return to our example above. It was shown that the PV of $1,000 ten years from now, assuming 10% interest rates year in and year out, was:

PV1000 = $1,000/(1 + 0.10)10 = $ 385.54

Now let’s let the expected path of interest rates be 5% year in and year out. What is the PV of $1,000 ten years from now given this lower expected path of interest rates?

PV1000 = $1,000/(1 + 0.05)10 = $ 613.91

So if the expected path of interest rates fall, all else constant, that should be good for stocks as the PV of the firm will rise.

Second, we can not ignore the influence of the change in the expected path of interest rates on expected profits. This influence is very real but also very hard to analyze and therefore, the context must be taken into account. For example, on one hand, lower interest rates in the future should stimulate economic activity and according to this version of the story, should result in higher expected profits. On the other hand, if people expect lower interest rates due to a poorly performing economy, then perhaps expected profits will fall instead of rise. So the influence of lower expected interest rates on the expectations of future profits is ambiguous, and thus, needs to be examined on a case by case basis.

Numerical Example and some Terminology

The stock price of any firm is equal to the (expected) present value of the firm (market cap) divided by the number of shares outstanding. Any factor, and there are many, that changes the expected present value of the firm, will change that stock price.[4]

The assumption (in the numerical example that follows) is that this firm falls off the face of the earth after three years, a more realistic example would include many more terms (an infinite amount!).

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Example:

|Company ABC (10,000 shares outstanding) |

|Year |1 |2 |3 |

|Exp. Earnings |$15,000 |$50,000 |$100,000 |

|Exp. 1 yr Interest Rate |0.03 |0.04 |0.05 |

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Price to earnings ratio (PE ratio): The price to earnings ratio is often used by investors as a guidepost as to whether a stock is “overvalued” or “undervalued.” Given that stock prices are determined by expectations of the future, we NEVER know whether a stock price is overvalued, undervalued, or valued ‘just right.’[5]

The price to earning ratio can be calculated in two equivalent ways:

1) Take the market cap, which is equal to the number of shares outstanding times the current price of the stock and divide it by current year earnings. From the example above:

PE ratio = $147,175 / $15,000 = 9.81

2) Take the price per share and divide it by current year earnings per share:

PE ratio = $14.72 / $1.50 = 9.81

We can now do some exercises:

1) Suppose the Federal Reserve makes a dovish announcement and as a result, investors expect the path of short term interest rates to be steady at 3% (as opposed to previous expectations over the three year life of the firm of 3, 4, and 5% respectively).

Exercise: What will happen to the Stock Price?[6]

Exercise: What will happen to the PE ratio?

2) Suppose the CEO of Company ABC makes a statement that the company’s expected earnings are now lower than previously expected (i.e., a pessimistic outlook) so that investors now expect profits to be ‘flat’ at $15,000 for the next three years (assume the initial expected path of interest rates of 3, 4, and 5% in year 1, 2, and 3 respectively).

Exercise: What will happen to the Stock Price?

Exercise: What will happen to the PE ratio?

3) Give two specific reasons why the PE ratio would be high for a firm and comment on the type of firm that may have a high PE ratio. Finally, does a high PE ratio imply that the firm is over valued? Why or why not?

The Optimal Forecast and Rational Expectations.

Example 1: Rational Expectations and a Question Before You Hand in Your Exam!

When I was at Grad School here at PSU, a professor told a story that I believe really clarifies exactly what we mean by rational expectations. Suppose I would say to the class before anyone handed in their exam (assume it is a multiple choice exam):

“Put an asterisk next to the three questions that you think you missed”

So let’s think about this for a moment……. which questions would you pick? The answer is that if you have rational expectations formation, you should not pick any! Why?? If you pick a question that you think you missed, then change the answer! Of course I know a lot of you are thinking that well…. some questions are harder than others and I will simply choose the three hardest questions! That is fine and consistent with rational expectations, but that is not admitting that you think you missed them because if you think you missed it, again, you would change the answer. So again, if I asked you how many questions you think you missed, your answer should be zero!

Another interesting and useful feature of this example is the concept of a probability distribution – some questions probably fall into the ‘no brainer’ category and thus, you are quite certain that you got them correct; some are in the easy but not that easy, etc. As we shall see, probability distributions and the associated uncertainty plays a critical role in financial markets and the economy.

Example 2: Using Rational Expectations on Your Drive to Work Each Day

Suppose you live in Port Matilda and work in State College. Suppose also that you do not want to arrive at work “too” early and you don’t want to arrive at work “too” late. Suppose through experience, you estimate the commute to be 15 minutes and thus leave 15 minutes before you are scheduled to work.[7] Suppose you begin work at 8 am and thus you leave at 7:45 am.

Questions:

1) Would you expect to get to work at starting time each and everyday?

2) Would you actually get to work at exactly the same time?

3) Is your forecast of the time it takes to get to work optimal? Why or why not?

Consider the following two scenarios:

a) One the way to work you get stuck in traffic due to an accident, somebody hit a deer and you end up getting to work 15 minutes late!

Question: Would you change your forecast on how long it takes to get to work and would this forecast be optimal?

b) The state begins construction (on the road you travel) and you are 15 minutes late for work. You learn that the construction is going to last for 6 months. Would you change your forecast on how long it takes to get to work and would this forecast be optimal?

Let’s define the forecast error (FE) as the starting time (8 am) minus (-) the actual arrival time. If the actual arrival time is 8am, then the forecast error equals zero; if the arrival time is not 8 am, then the FE is non-zero. What are the properties of this forecast error (there are three of them)?

a.

b.

c.

Predicting Tomorrow’s Stock Price and the Efficient Market Theory

In the driving to work example above, we had the incentive to obtain an optimal forecast for the commute and thus, we used all the relevant information available to formulate that optimal forecast. For example, if it snowed all night and you believed the roads are likely to be slippery, you would use that relevant and available information immediately and incorporate (process the information) it into your forecast of the time it will take to get to work. In terms of jargon, we would say you were irrational if you did not account for the snowfall.

Naturally, any investor would love to be able to predict the future, because if you can predict future movements in asset prices, you could place the appropriate bet(s) and make lots of money! The example that follows applies to stocks, but the same line of reasoning can be applied to the bond and foreign exchange markets.

Suppose you were to try to predict tomorrow’s stock price today. Let us define the information set available to you today as Ωt. Naturally, Ωt contains ALL information that is available at time t, where the subscript t stands for today, the subscript t+1 stands for tomorrow (next period in general).

We can write the following:

St+1 = f (Ωt):

{stated as: “Tomorrow’s stock price is a function of the (entire) information set available today.”}

Naturally, we would want to use all the relevant information that is currently available in predicting an asset price. Another way to say this is that it would be irrational if we did not use all the relevant and available information that was available today (recall the drive to work and ignoring the snowfall example). In fact, rational expectations formation simply means that agents use all the information that is available today in making their forecasts and thus, the forecast is optimal.

Predicting stock prices is very similar in that you rationally use all the relevant information that is available to you when formulating your optimal forecast.

Predicting Stock Prices: A forecasting model

In the equation below, we could add a plethora of information that is available today.[8] Naturally, we would want to use only the relevant information but how do we know what information is relevant and what information is not? In the equation below, ie stands for expected interest rates, UR for unemployment rates, CC for consumer confidence, GDP for gross domestic product, HS for housing starts, etc. Naturally, we could just keep on adding variables to the model and thus, the forecasting model will become very complex (Ωt is extremely large). Thankfully, we have the efficient market theory to make ‘life’ much easier.

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THE EFFICIENT MARKET THEORY

Definition: If markets are efficient, then the current asset price has already incorporated all the relevant and available information related to that asset. Furthermore, if markets are efficient, then NEWS, as defined as the ‘unexpected,’ is immediately reflected in the asset price. That is, asset prices process new information very quickly and accurately (as in the snowfall and commute to work example).

Implications of the efficient market theory – since efficient markets imply that the current asset price has already incorporated all the relevant and currently available information, then it would be a waste of our time (fruitless) building fancy and complex models to predict future asset prices, since today’s price has already processed all the current, relevant and available information. The good news is that it makes our forecasting equation very simple. The bad news is that in order to predict changes the stock price, we would need to predict the unexpected; e.g., we would need a crystal ball.[9] Good luck with that!

Best forecasting equation assuming efficient markets:

St+1 = f (St)

In other words, the best predictor of tomorrow’s stock price is today’s stock price. This fact supports the Efficient Market Theory which states that today’s stock price contains all current and relevant information associated with the fundamental value of the firm that is available today (it efficiently processes what is in Ωt). According to efficient markets, the only reason that tomorrow’s stock price will differ from today’s would be due to NEWS that occurs between today and tomorrow. So, in effect, the NEWS is exactly equal to FE, which is defined as the forecast error. If there is no news then FE=zero, and St = St+1.[10]

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Properties of the forecast error, assuming efficient markets (recall commute to work ex.).

1. The FE must have a mean of zero (we assume that good news is as likely as bad news).

2. The FE must be independent of Ωt, where Ωt is the entire information set that is available at time t. If FE is not independent, that implies that St is not processing all the relevant and available information contained in Ωt, and thus, violates the assumption of the efficient market theory.

3. The FE must be uncorrelated with past FE’s (serially uncorrelated). Another way to state this is that NEWs is completely absorbed immediately so that today’s forecast error does not help us predict tomorrows forecast error. Recall specifically the commute to work example when there was a 1) accident that resulted in being late for work and 2) the road construction. Even though these was a large forecast error (we were really late for work), does that forecast error help us predict the forecast error tomorrow. The answer is no, the expected forecast error would again be zero, since rational expectations formation ensures that we use all relevant information available.

TESTING THE EFFICIENT MARKET THEORY (EMT)

My goal in what follows is to give you a clue as to what many economists do for a living, and that is, crunch numbers! A good amount of economic research is theoretical, and a good amount of economic research is empirical. I much prefer empirical analysis, and empirical analysis is often utilized to test (prove or disprove) economic theories.[11]

A Primer on Regression Analysis: A Consumption Function Example

The example below should be a little familiar to you from econ 004. Consumption accounts for about 70% of GDP and is thus, very much studied by economists and other economic actors interested in understanding and predicting economic activity. In econ 004 you should, at the very least, recall that disposable income and the level of consumption are tightly related, that is, if we have data on disposable income, then we can make pretty good guesses as to the level of consumption. You should also recall that consumption is also influenced by other factors as well. In what follows, we develop a fairly realistic model of consumption, and then we simplify it when interpreting the empirical results.

Consumption Function

[pic]

where:

Yd is personal disposable income

WSM is wealth in the stock market

WRE is wealth in real estate

r is the real interest rate

EX is the exchange rate where an increase implies the dollar is appreciating

CC is consumer confidence

If we used all the variables (above) to predict consumption, the regression equation will take the following form:

[pic]

The ai’s are sensitivity parameters. They tell us which direction and by how much consumption is affected by changes in each of the variables. For instance, a1 is the marginal propensity to consume (MPC), and tells us how sensitive consumption is to changes in disposable income.[12]

Empirical Results – The Consumption Function

The set up: I estimate a consumption function that includes all the arguments: above except for the exchange rate. The purpose of this example is to get you familiar with the usefulness and interpretation of these empirical results.

Important features of regression output:

R2 represents the fit of the model; the higher the R2, the better the fit. The maximum value for R2 is 1.00 and the minimum value is zero.

t-stats; if the absolute value of the t-stat exceeds 2.00, then we say that the associated variable ‘belongs’ in the regression. t-stats basically test whether or not a coefficient is significantly different than zero. If the t-stat exceeds two, then the coefficient is said to be ‘statistically different than zero.’

Coefficient interpretation: We are typically interested in the sign of the coefficient (i.e., is it consistent with economic theory) as well as the size (this has to do with economic significance). Example: the MPC (a1) in the equation above should be positive, close to one, and significant.[13]

Empirical Results on the consumption function

Equation estimated

C = a0 + a1 Yd + a2 r + a3 WSM + a4 WRE + a5 CC

Priors:

a1 is the marginal propensity to consume and should be somewhere around 0.9 in value and very significant (high t-statistic) since we know there does exist a tight relationship between consumption and disposable income.

a2 should be negative since the lower the real rate of interest, the less in pays to save (i.e., consume!).

a3 should be positive and significant – i.e., the wealth effect in terms of stock market wealth.

a4 should be positive and significant – i.e., the wealth effect in terms of real estate wealth. Note also that the claim is that a4 should be greater than a3, that is, dollar for dollar, the wealth effect in real estate is great than the wealth effect in stocks since changes in the former (real estate wealth) are perceived by economic agents to be more permanent and stable than the latter (changes in stock market wealth ,’here today, gone tomorrow.’

a5 should be positive, the more confident you are, the more you consume!

Also, the overall fit should be quite good, since we know that there is tight relationship between C and Yd

Regression Output: 1977Q3 – 2006Q2

C = -115 + .788(Yd) – 10.486(r) + .032(WSM) + .078(WRE) + .516(CC)

|Dependent Variable: Consumption |

|Method: Least Squares |

|Date: 04/23/07 Time: 19:04 |

|Sample: 1977:3 2006:2 |

|Included observations: 116 |

| | | | | |

|Variable |Coefficient |Std. Error |t-Statistic |Prob. |

| | | | | |

|C |-115.9823 |31.78627 |-3.648819 |0.0004 |

|Yd(-1) |0.787909 |0.015640 |50.37847 |0.0000 |

|r (-1) |-10.48553 |2.276948 |-4.605081 |0.0000 |

|WSM(-1) |0.032054 |0.005459 |5.871944 |0.0000 |

|WRE(-1) |0.078031 |0.005771 |13.52198 |0.0000 |

|CC(-1) |0.515951 |0.279377 |1.846792 |0.0675 |

| | | | | |

|R-squared |0.999554 | Mean dependent var |4512.648 |

|Adjusted R-squared |0.999534 | S.D. dependent var |2243.232 |

|S.E. of regression |48.44171 | Akaike info criterion |10.64894 |

|Sum squared resid |258125.9 | Schwarz criterion |10.79136 |

|Log likelihood |-611.6384 | F-statistic |49299.63 |

|Durbin-Watson stat |0.802282 | Prob(F-statistic) |0.000000 |

| | | | | |

We will interpret all of this in class!

Testing of the efficient market hypothesis

S = closing price of Google Stock. Daily Data from Yahoo!!

The data: Daily Data from August 20, 2004 – August 30, 2007 (790 observations)

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Equation estimated

(1) St+1 = α + β St + FEt+1

which is, if you back date (go back one day ), the same as

(2) St = α + β St-1 + FEt

Equation (2) is the equation that is estimated: What are our priors?

α should be positive, yet small, and should represent the “equilibrium” market return

β should be one, implying that the difference between today’s and tomorrows spot price is (ignoring α for a second) equal to FEt+1.

We are going to test here shortly the properties of FEt+1. Recall what they are?

1)

2)

3)

But first, let’s look at some results predicting tomorrow’s stock price with todays!

Check out the fit!

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Equation Estimated: St = α + β St-1 + FEt

|Dependent Variable: GOOG |

|Method: Least Squares |

|Date: 10/09/07 Time: 23:01 |

|Sample(adjusted): 8/20/2004 8/30/2007 |

|Included observations: 790 after adjusting endpoints |

|Variable |Coefficient |Std. Error |t-Statistic |Prob. |

|C |1.222339 |0.748589 |1.632858 |0.1029 |

|GOOG(-1) |0.998410 |0.001970 |506.8233 |0.0000 |

|R-squared |0.996942 | Mean dependent var |359.5207 |

|Adjusted R-squared |0.996938 | S.D. dependent var |125.0430 |

|S.E. of regression |6.919524 | Akaike info criterion |6.709099 |

|Sum squared resid |37729.29 | Schwarz criterion |6.720927 |

|Log likelihood |-2648.094 | F-statistic |256869.8 |

|Durbin-Watson stat |1.911456 | Prob(F-statistic) |0.000000 |

Note that β is very close to one and the fit is very good!

Lets try to improve the fit by adding more “Cats and Dogs” to the right hand side of the equation.

|Dependent Variable: GOOG |

|Method: Least Squares |

|Date: 10/09/07 Time: 22:55 |

|Sample(adjusted): 8/27/2004 8/29/2007 |

|Included observations: 784 after adjusting endpoints |

|Variable |Coefficient |Std. Error |t-Statistic |Prob. |

|C |2.977423 |4.155744 |0.716460 |0.4739 |

|GOOG(-1) |1.039484 |0.036204 |28.71193 |0.0000 |

|GOOG(-2) |-0.017874 |0.052057 |-0.343355 |0.7314 |

|GOOG(-3) |-0.045028 |0.052110 |-0.864088 |0.3878 |

|GOOG(-4) |0.079843 |0.052103 |1.532399 |0.1258 |

|GOOG(-5) |-0.071880 |0.052165 |-1.377945 |0.1686 |

|GOOG(-6) |0.014510 |0.036306 |0.399663 |0.6895 |

|YIELD10YR(-1) |1.818302 |5.814346 |0.312727 |0.7546 |

|YIELD10YR(-2) |2.780892 |8.115906 |0.342647 |0.7320 |

|YIELD10YR(-3) |-1.921781 |8.096711 |-0.237353 |0.8124 |

|YIELD10YR(-4) |-3.839147 |8.113601 |-0.473174 |0.6362 |

|YIELD10YR(-5) |1.075725 |8.157192 |0.131874 |0.8951 |

|YIELD10YR(-6) |-0.365652 |5.839052 |-0.062622 |0.9501 |

|R-squared |0.996877 | Mean dependent var |360.8032 |

|Adjusted R-squared |0.996828 | S.D. dependent var |123.5483 |

|S.E. of regression |6.958013 | Akaike info criterion |6.734107 |

|Sum squared resid |37327.15 | Schwarz criterion |6.811451 |

|Log likelihood |-2626.770 | F-statistic |20508.10 |

|Durbin-Watson stat |1.994819 | Prob(F-statistic) |0.000000 |

Note – nothing helps! The only significant predictor is today’s stock price! Is this consistent with the efficient market theory????

We now exam the properties of FE!

Let try to predict it with Ωt

|Dependent Variable: FE |

|Method: Least Squares |

|Date: 10/10/07 Time: 07:15 |

|Sample(adjusted): 8/27/2004 8/29/2007 |

|Included observations: 784 after adjusting endpoints |

|Variable |Coefficient |Std. Error |t-Statistic |Prob. |

|C |2.977423 |4.155744 |0.716460 |0.4739 |

|GOOG(-1) |0.039484 |0.036204 |1.090603 |0.2758 |

|GOOG(-2) |-0.017874 |0.052057 |-0.343355 |0.7314 |

|GOOG(-3) |-0.045028 |0.052110 |-0.864088 |0.3878 |

|GOOG(-4) |0.079843 |0.052103 |1.532399 |0.1258 |

|GOOG(-5) |-0.071880 |0.052165 |-1.377945 |0.1686 |

|GOOG(-6) |0.014510 |0.036306 |0.399663 |0.6895 |

|YIELD10YR(-1) |1.818302 |5.814346 |0.312727 |0.7546 |

|YIELD10YR(-2) |2.780892 |8.115906 |0.342647 |0.7320 |

|YIELD10YR(-3) |-1.921781 |8.096711 |-0.237353 |0.8124 |

|YIELD10YR(-4) |-3.839147 |8.113601 |-0.473174 |0.6362 |

|YIELD10YR(-5) |1.075725 |8.157192 |0.131874 |0.8951 |

|YIELD10YR(-6) |-0.365652 |5.839052 |-0.062622 |0.9501 |

|R-squared |0.008677 | Mean dependent var |0.639936 |

|Adjusted R-squared |-0.006752 | S.D. dependent var |6.934641 |

|S.E. of regression |6.958013 | Akaike info criterion |6.734107 |

|Sum squared resid |37327.15 | Schwarz criterion |6.811451 |

|Log likelihood |-2626.770 | F-statistic |0.562386 |

|Durbin-Watson stat |1.994819 | Prob(F-statistic) |0.872886 |

THE FIT IS TERRIBLE – R2 = 0.008677, We can’t predict the change in price of Google between today and tomorrow with today’s information set.

NOW LETS TRY TO PREDICT FE WITH ITS PAST

|Dependent Variable: FE |

|Method: Least Squares |

|Date: 10/10/07 Time: 07:14 |

|Sample(adjusted): 8/30/2004 8/30/2007 |

|Included observations: 784 after adjusting endpoints |

|Variable |Coefficient |Std. Error |t-Statistic |Prob. |

|C |0.606648 |0.253054 |2.397310 |0.0168 |

|FE(-1) |0.043617 |0.035867 |1.216089 |0.2243 |

|FE(-2) |0.028162 |0.035995 |0.782389 |0.4342 |

|FE(-3) |-0.022462 |0.036045 |-0.623170 |0.5334 |

|FE(-4) |0.057552 |0.036051 |1.596412 |0.1108 |

|FE(-5) |-0.013378 |0.036096 |-0.370624 |0.7110 |

|FE(-6) |-0.025935 |0.036047 |-0.719473 |0.4721 |

|R-squared |0.006995 | Mean dependent var |0.649273 |

|Adjusted R-squared |-0.000673 | S.D. dependent var |6.936333 |

|S.E. of regression |6.938667 | Akaike info criterion |6.720985 |

|Sum squared resid |37408.74 | Schwarz criterion |6.762631 |

|Log likelihood |-2627.626 | F-statistic |0.912226 |

|Durbin-Watson stat |2.004756 | Prob(F-statistic) |0.485310 |

SAME KIND OF STORY, PAST FORECAST ERRORS DO NOT HELP PREDICT FUTURE FORECAST ERRORS

ALL TOLD – IT IS IMPOSSIBLE TO PREDICT CHANGES IN THE SPOT PRICE OF GOOGLE

Does FE have mean of zero???

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Summary: Our empirical results are consistent with the efficient market theory implying that it is impossible to predict changes in stock prices, suggesting that the closing price of coke follows a random walk.[14]

Another way to state this is that it is impossible to “beat the market.”

Updated results

SAMPLE - DAILY DATA - 1/2/2007

VARIABLES

DAAA: Moody's Seasoned Aaa Corporate Bond Yield

DBAA: Moody's Seasoned Baa Corporate Bond Yield

DGS10: 10-Year Treasury Constant Maturity Rate

DGS3MO: 3-Month Treasury Constant Maturity Rate

DJIA: Dow Jones Industrial Average

SP500: S&P 500 Stock Price Index

VIXCLS: CBOE Volatility Index: VIX

CPN3M: 3-Month AA Nonfinancial Commercial Paper Rate

VIX measures market expectation of near term volatility conveyed by

stock index option prices. Copyright, 2011, Chicago Board Options

Exchange, Inc. Reprinted with permission.

VXDCLS: CBOE DJIA Volatility Index

WILL5000IND: Wilshire 5000 Total Market Index

INTEREST RATE SPREADS - 'HAND" CALCULATED

"risk structure spreads"

paperbillspread = rate on 3 month paper minus rate on 3 month Tbill

corpspread = rate on baa minus aaa

yield spread

slopeyc = rate on 10 year Treasury minus 3 month Tbill

LET'S LOOK AT THE DATA!

OUR DEPENDENT VARIABLE - WHAT WE ARE TRYING TO PREDICT!

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SPREADS

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CORPSREAD AND DJIA AVERAGE TOGETHER

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RUN A REGRESSION - PRIORS????

|Dependent Variable: DJIA | | |

|Method: Least Squares | | |

|Date: 10/11/13 Time: 07:10 | | |

|Sample (adjusted): 1/03/2007 10/04/2013 | |

|Included observations: 1633 after adjustments | |

|White Heteroskedasticity-Consistent Standard Errors & Covariance |

| | | | | |

| | | | | |

|Variable |Coefficient |Std. Error |t-Statistic |Prob.   |

| | | | | |

| | | | | |

|C |14837.08 |75.28027 |197.0912 |0.0000 |

|CORPSPREAD(-1) |-2298.243 |47.85215 |-48.02801 |0.0000 |

| | | | | |

| | | | | |

|R-squared |0.501559 |    Mean dependent var |11855.05 |

|Adjusted R-squared |0.501253 |    S.D. dependent var |1909.018 |

|S.E. of regression |1348.186 |    Akaike info criterion |17.25213 |

|Sum squared resid |2.96E+09 |    Schwarz criterion |17.25874 |

|Log likelihood |-14084.37 |    Hannan-Quinn criter. |17.25458 |

|F-statistic |1641.203 |    Durbin-Watson stat |0.013821 |

|Prob(F-statistic) |0.000000 | | | |

| | | | | |

| | | | | |

A LOOK AT THE FITTED VALUES, ACTUAL VALUES AND THE RESIDUALS

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VIX

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|Dependent Variable: DJIA | | |

|Method: Least Squares | | |

|Date: 10/11/13 Time: 07:15 | | |

|Sample (adjusted): 1/04/2007 10/04/2013 | |

|Included observations: 1640 after adjustments | |

|White Heteroskedasticity-Consistent Standard Errors & Covariance |

| | | | | |

| | | | | |

|Variable |Coefficient |Std. Error |t-Statistic |Prob.   |

| | | | | |

| | | | | |

|C |14839.96 |99.19846 |149.5987 |0.0000 |

|VIXCLS(-1) |-128.3368 |4.361714 |-29.42348 |0.0000 |

| | | | | |

| | | | | |

|R-squared |0.514798 |    Mean dependent var |11851.36 |

|Adjusted R-squared |0.514501 |    S.D. dependent var |1910.515 |

|S.E. of regression |1331.203 |    Akaike info criterion |17.22677 |

|Sum squared resid |2.90E+09 |    Schwarz criterion |17.23336 |

|Log likelihood |-14123.95 |    Hannan-Quinn criter. |17.22922 |

|F-statistic |1737.911 |    Durbin-Watson stat |0.062123 |

|Prob(F-statistic) |0.000000 | | | |

| | | | | |

| | | | | |

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Both together

|Dependent Variable: DJIA | | |

|Method: Least Squares | | |

|Date: 10/11/13 Time: 07:17 | | |

|Sample (adjusted): 1/04/2007 10/04/2013 | |

|Included observations: 1629 after adjustments | |

|White Heteroskedasticity-Consistent Standard Errors & Covariance |

| | | | | |

| | | | | |

|Variable |Coefficient |Std. Error |t-Statistic |Prob.   |

| | | | | |

| | | | | |

|C |15174.71 |92.57123 |163.9247 |0.0000 |

|CORPSPREAD(-1) |-1205.753 |72.93067 |-16.53287 |0.0000 |

|VIXCLS(-1) |-75.51517 |5.220112 |-14.46620 |0.0000 |

| | | | | |

| | | | | |

|R-squared |0.565048 |    Mean dependent var |11854.11 |

|Adjusted R-squared |0.564513 |    S.D. dependent var |1910.907 |

|S.E. of regression |1261.035 |    Akaike info criterion |17.11909 |

|Sum squared resid |2.59E+09 |    Schwarz criterion |17.12903 |

|Log likelihood |-13940.50 |    Hannan-Quinn criter. |17.12278 |

|F-statistic |1056.172 |    Durbin-Watson stat |0.034814 |

|Prob(F-statistic) |0.000000 | | | |

| | | | | |

| | | | | |

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LET'S ADD SOME MORE 'CATS AND DOGS'

|Dependent Variable: DJIA | | |

|Method: Least Squares | | |

|Date: 10/11/13 Time: 07:20 | | |

|Sample (adjusted): 1/04/2007 10/04/2013 | |

|Included observations: 1583 after adjustments | |

|White Heteroskedasticity-Consistent Standard Errors & Covariance |

| | | | | |

| | | | | |

|Variable |Coefficient |Std. Error |t-Statistic |Prob.   |

| | | | | |

| | | | | |

|C |16168.56 |103.1214 |156.7915 |0.0000 |

|CORPSPREAD(-1) |-1247.905 |57.17984 |-21.82422 |0.0000 |

|VIXCLS(-1) |-86.68247 |5.108776 |-16.96737 |0.0000 |

|PAPERBILLSPREAD(-1) |674.9472 |40.23692 |16.77433 |0.0000 |

|SLOPEYC(-1) |-449.4423 |28.91532 |-15.54340 |0.0000 |

| | | | | |

| | | | | |

|R-squared |0.666942 |    Mean dependent var |11933.80 |

|Adjusted R-squared |0.666098 |    S.D. dependent var |1867.028 |

|S.E. of regression |1078.849 |    Akaike info criterion |16.80833 |

|Sum squared resid |1.84E+09 |    Schwarz criterion |16.82528 |

|Log likelihood |-13298.79 |    Hannan-Quinn criter. |16.81463 |

|F-statistic |789.9790 |    Durbin-Watson stat |0.053805 |

|Prob(F-statistic) |0.000000 | | | |

SO THESE RHS VARIABLES ARE ALL PART OF THE INFORMATION SET

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LET'S ADD THE OBVIOUS - a lagged DJIA term

|Dependent Variable: DJIA | | |

|Method: Least Squares | | |

|Date: 10/11/13 Time: 07:23 | | |

|Sample (adjusted): 1/04/2007 10/04/2013 | |

|Included observations: 1582 after adjustments | |

|White Heteroskedasticity-Consistent Standard Errors & Covariance |

| | | | | |

| | | | | |

|Variable |Coefficient |Std. Error |t-Statistic |Prob.   |

| | | | | |

| | | | | |

|C |26.39219 |59.36265 |0.444593 |0.6567 |

|CORPSPREAD(-1) |-17.51524 |13.44292 |-1.302935 |0.1928 |

|VIXCLS(-1) |1.845633 |1.176906 |1.568207 |0.1170 |

|PAPERBILLSPREAD(-1) |-28.88434 |14.17016 |-2.038392 |0.0417 |

|SLOPEYC(-1) |-6.238820 |3.475534 |-1.795068 |0.0728 |

|DJIA(-1) |0.998321 |0.003233 |308.8019 |0.0000 |

| | | | | |

| | | | | |

|R-squared |0.994691 |    Mean dependent var |11933.10 |

|Adjusted R-squared |0.994674 |    S.D. dependent var |1867.416 |

|S.E. of regression |136.2845 |    Akaike info criterion |12.67115 |

|Sum squared resid |29271790 |    Schwarz criterion |12.69151 |

|Log likelihood |-10016.88 |    Hannan-Quinn criter. |12.67871 |

|F-statistic |59052.57 |    Durbin-Watson stat |2.144099 |

|Prob(F-statistic) |0.000000 | | | |

| | | | | |

| | | | | |

CHECK OUT THE POWER OF YESTERDAY'S DJIA IN THE MODEL!

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LET'S

TESTING THE EFFICIENT MARKET THEORY

|Dependent Variable: DJIA | | |

|Method: Least Squares | | |

|Date: 10/10/13 Time: 12:55 | | |

|Sample (adjusted): 1/04/2007 10/04/2013 | |

|Included observations: 1639 after adjustments | |

|White Heteroskedasticity-Consistent Standard Errors & Covariance |

| | | | | |

| | | | | |

|Variable |Coefficient |Std. Error |t-Statistic |Prob.   |

| | | | | |

| | | | | |

|C |27.80542 |26.44765 |1.051338 |0.2933 |

|DJIA(-1) |0.997742 |0.002098 |475.6008 |0.0000 |

| | | | | |

| | | | | |

|R-squared |0.994459 |    Mean dependent var |11850.64 |

|Adjusted R-squared |0.994456 |    S.D. dependent var |1910.876 |

|S.E. of regression |142.2824 |    Akaike info criterion |12.75472 |

|Sum squared resid |33139872 |    Schwarz criterion |12.76132 |

|Log likelihood |-10450.50 |    Hannan-Quinn criter. |12.75717 |

|F-statistic |293808.2 |    Durbin-Watson stat |2.218066 |

|Prob(F-statistic) |0.000000 | | | |

| | | | | |

| | | | | |

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ADD LAGS

|Dependent Variable: DJIA | | |

|Method: Least Squares | | |

|Date: 10/10/13 Time: 12:56 | | |

|Sample (adjusted): 1/30/2007 10/04/2013 | |

|Included observations: 1114 after adjustments | |

|White Heteroskedasticity-Consistent Standard Errors & Covariance |

| | | | | |

| | | | | |

|Variable |Coefficient |Std. Error |t-Statistic |Prob.   |

| | | | | |

| | | | | |

|C |41.65038 |30.70866 |1.356308 |0.1753 |

|DJIA(-1) |0.874143 |0.043242 |20.21502 |0.0000 |

|DJIA(-2) |0.081718 |0.067250 |1.215134 |0.2246 |

|DJIA(-3) |0.047933 |0.065094 |0.736358 |0.4617 |

|DJIA(-4) |-0.013973 |0.061607 |-0.226812 |0.8206 |

|DJIA(-5) |-0.020373 |0.063273 |-0.321994 |0.7475 |

|DJIA(-6) |0.023064 |0.072414 |0.318501 |0.7502 |

|DJIA(-7) |-0.036536 |0.067062 |-0.544818 |0.5860 |

|DJIA(-8) |0.102430 |0.070459 |1.453754 |0.1463 |

|DJIA(-9) |-0.074870 |0.069470 |-1.077729 |0.2814 |

|DJIA(-10) |0.012848 |0.049960 |0.257175 |0.7971 |

| | | | | |

| | | | | |

|R-squared |0.994211 |    Mean dependent var |11839.00 |

|Adjusted R-squared |0.994158 |    S.D. dependent var |1929.595 |

|S.E. of regression |147.4832 |    Akaike info criterion |12.83513 |

|Sum squared resid |23991675 |    Schwarz criterion |12.88466 |

|Log likelihood |-7138.168 |    Hannan-Quinn criter. |12.85386 |

|F-statistic |18941.78 |    Durbin-Watson stat |2.026282 |

|Prob(F-statistic) |0.000000 | | | |

| | | | | |

| | | | | |

NOTE - NONE OF THE ADDED LAGS ARE SIGNIFICANT - THE FIT HAS NOT CHANGED

LET'S CHECK OUT THE RESIDUALS - THE FORECAST ERRORS - SAME AS PREDICTING THE CHANGE IN THE DJIA FROM ONE DAY TO THE NEXT"

|Dependent Variable: FE | | |

|Method: Least Squares | | |

|Date: 10/11/13 Time: 07:46 | | |

|Sample (adjusted): 1/04/2007 10/04/2013 | |

|Included observations: 1582 after adjustments | |

|White Heteroskedasticity-Consistent Standard Errors & Covariance |

| | | | | |

| | | | | |

|Variable |Coefficient |Std. Error |t-Statistic |Prob.   |

| | | | | |

| | | | | |

|C |60.86573 |44.64669 |1.363275 |0.1730 |

|DJIA(-1) |-0.003049 |0.002490 |-1.224893 |0.2208 |

|CORPSPREAD(-1) |-3.948232 |12.29165 |-0.321213 |0.7481 |

|PAPERBILLSPREAD(-1) |-18.76430 |13.35854 |-1.404667 |0.1603 |

|SLOPEYC(-1) |-5.431679 |3.444850 |-1.576753 |0.1151 |

| | | | | |

| | | | | |

|R-squared |0.005825 |    Mean dependent var |0.688103 |

|Adjusted R-squared |0.003303 |    S.D. dependent var |136.7859 |

|S.E. of regression |136.5597 |    Akaike info criterion |12.67456 |

|Sum squared resid |29408787 |    Schwarz criterion |12.69152 |

|Log likelihood |-10020.57 |    Hannan-Quinn criter. |12.68086 |

|F-statistic |2.309998 |    Durbin-Watson stat |2.176839 |

|Prob(F-statistic) |0.055856 | | | |

| | | | | |

| | | | | |

AS YOU CAN SEE, YOU CANNOT PREDICT THE FORECAST ERROR TODAY, WITH INFORMATION YESTERDAY! HERE WE SAY TODAY'S FORECAST ERROR IS ORTHOGONAL TO YESTERDAY'S INFORMATION SET - WE DID THE BEST WE COULD - THIS NEWS IS UNPREDICTABLE!

LET'S CHECK TO SEE IF THE FORECAST ERRORS ARE AUTO-CORRELATED - THAT IS, DO THEY HAVE A PATTERN

|Dependent Variable: FE | | |

|Method: Least Squares | | |

|Date: 10/11/13 Time: 07:52 | | |

|Sample (adjusted): 1/05/2007 10/04/2013 | |

|Included observations: 1577 after adjustments | |

|Newey-West HAC Standard Errors & Covariance (lag truncation=7) |

| | | | | |

| | | | | |

|Variable |Coefficient |Std. Error |t-Statistic |Prob.   |

| | | | | |

| | | | | |

|C |0.310619 |3.417839 |0.090882 |0.9276 |

|FE(-1) |-0.104658 |0.032695 |-3.200989 |0.0014 |

| | | | | |

| | | | | |

|R-squared |0.011214 |    Mean dependent var |0.366532 |

|Adjusted R-squared |0.010586 |    S.D. dependent var |141.6477 |

|S.E. of regression |140.8960 |    Akaike info criterion |12.73519 |

|Sum squared resid |31266408 |    Schwarz criterion |12.74199 |

|Log likelihood |-10039.70 |    Hannan-Quinn criter. |12.73772 |

|F-statistic |17.86160 |    Durbin-Watson stat |2.031995 |

|Prob(F-statistic) |0.000025 | | | |

| | | | | |

| | | | | |

HERE WE HAVE A SLIGHT VIOLATION OF THE EMT - INTERPRET??

ADD MORE LAGS - NOT MUCH HELP

|Dependent Variable: FE | | |

|Method: Least Squares | | |

|Date: 10/11/13 Time: 07:54 | | |

|Sample (adjusted): 1/11/2007 10/04/2013 | |

|Included observations: 1339 after adjustments | |

|Newey-West HAC Standard Errors & Covariance (lag truncation=7) |

| | | | | |

| | | | | |

|Variable |Coefficient |Std. Error |t-Statistic |Prob.   |

| | | | | |

| | | | | |

|C |-0.334619 |3.864469 |-0.086589 |0.9310 |

|FE(-1) |-0.111541 |0.038642 |-2.886483 |0.0040 |

|FE(-2) |-0.042194 |0.052573 |-0.802573 |0.4224 |

|FE(-3) |0.011283 |0.041409 |0.272488 |0.7853 |

|FE(-4) |-0.016290 |0.040956 |-0.397734 |0.6909 |

|FE(-5) |-0.026073 |0.046839 |-0.556660 |0.5779 |

| | | | | |

| | | | | |

|R-squared |0.014599 |    Mean dependent var |-0.302586 |

|Adjusted R-squared |0.010903 |    S.D. dependent var |144.2587 |

|S.E. of regression |143.4701 |    Akaike info criterion |12.77460 |

|Sum squared resid |27438023 |    Schwarz criterion |12.79790 |

|Log likelihood |-8546.595 |    Hannan-Quinn criter. |12.78333 |

|F-statistic |3.949889 |    Durbin-Watson stat |2.049769 |

|Prob(F-statistic) |0.001468 | | | |

| | | | | |

| | | | | |

LET'S CHECK OUT THE ERRORS FROM THE MODEL WITHOUT DJIA - I COPY AND PASTE FROM ABOVE

|Dependent Variable: DJIA | | |

|Method: Least Squares | | |

|Date: 10/11/13 Time: 07:20 | | |

|Sample (adjusted): 1/04/2007 10/04/2013 | |

|Included observations: 1583 after adjustments | |

|White Heteroskedasticity-Consistent Standard Errors & Covariance |

| | | | | |

| | | | | |

|Variable |Coefficient |Std. Error |t-Statistic |Prob.   |

| | | | | |

| | | | | |

|C |16168.56 |103.1214 |156.7915 |0.0000 |

|CORPSPREAD(-1) |-1247.905 |57.17984 |-21.82422 |0.0000 |

|VIXCLS(-1) |-86.68247 |5.108776 |-16.96737 |0.0000 |

|PAPERBILLSPREAD(-1) |674.9472 |40.23692 |16.77433 |0.0000 |

|SLOPEYC(-1) |-449.4423 |28.91532 |-15.54340 |0.0000 |

| | | | | |

| | | | | |

|R-squared |0.666942 |    Mean dependent var |11933.80 |

|Adjusted R-squared |0.666098 |    S.D. dependent var |1867.028 |

|S.E. of regression |1078.849 |    Akaike info criterion |16.80833 |

|Sum squared resid |1.84E+09 |    Schwarz criterion |16.82528 |

|Log likelihood |-13298.79 |    Hannan-Quinn criter. |16.81463 |

|F-statistic |789.9790 |    Durbin-Watson stat |0.053805 |

|Prob(F-statistic) |0.000000 | | | |

SO THESE RHS VARIABLES ARE ALL PART OF THE INFORMATION SET

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I LABELED THESE ERRORS AS WITHOUTDJIARESIDS

|Dependent Variable: WITHOUTDJIARESIDS | |

|Method: Least Squares | | |

|Date: 10/11/13 Time: 08:01 | | |

|Sample (adjusted): 1/04/2007 10/04/2013 | |

|Included observations: 1582 after adjustments | |

|Newey-West HAC Standard Errors & Covariance (lag truncation=7) |

| | | | | |

| | | | | |

|Variable |Coefficient |Std. Error |t-Statistic |Prob.   |

| | | | | |

| | | | | |

|C |-3919.148 |494.1908 |-7.930436 |0.0000 |

|DJIA(-1) |0.328474 |0.040920 |8.027284 |0.0000 |

| | | | | |

| | | | | |

|R-squared |0.323801 |    Mean dependent var |0.057241 |

|Adjusted R-squared |0.323373 |    S.D. dependent var |1077.822 |

|S.E. of regression |886.5876 |    Akaike info criterion |16.41390 |

|Sum squared resid |1.24E+09 |    Schwarz criterion |16.42068 |

|Log likelihood |-12981.40 |    Hannan-Quinn criter. |16.41642 |

|F-statistic |756.5915 |    Durbin-Watson stat |0.099424 |

|Prob(F-statistic) |0.000000 | | | |

| | | | | |

| | | | | |

SO THERE IS INFORMATION AVAILABLE IN YESTERDAY'S INFORMATION SET THAT IS NOT BEING USED - VIOLATION OF THE EMT

DO THESE ERRORS HAVE A PATTERN?

|Dependent Variable: WITHOUTDJIARESIDS | |

|Method: Least Squares | | |

|Date: 10/11/13 Time: 08:04 | | |

|Sample (adjusted): 1/05/2007 10/04/2013 | |

|Included observations: 1494 after adjustments | |

|Newey-West HAC Standard Errors & Covariance (lag truncation=7) |

| | | | | |

| | | | | |

|Variable |Coefficient |Std. Error |t-Statistic |Prob.   |

| | | | | |

| | | | | |

|C |1.787490 |3.933498 |0.454428 |0.6496 |

|WITHOUTDJIARESIDS(-1) |0.976777 |0.005286 |184.7729 |0.0000 |

| | | | | |

| | | | | |

|R-squared |0.946850 |    Mean dependent var |-8.203185 |

|Adjusted R-squared |0.946815 |    S.D. dependent var |1079.034 |

|S.E. of regression |248.8461 |    Akaike info criterion |13.87288 |

|Sum squared resid |92391176 |    Schwarz criterion |13.87999 |

|Log likelihood |-10361.04 |    Hannan-Quinn criter. |13.87553 |

|F-statistic |26579.66 |    Durbin-Watson stat |2.849583 |

|Prob(F-statistic) |0.000000 | | | |

| | | | | |

| | | | | |

YES!!! THE ERRORS FROM THE INCOMPLETE MODEL ARE HIGHLY AUTOCORRELATED - IF POSITIVE TODAY, POSITIVE TOMORROW AND VICA VERSA

The Wall Street Journal tested this random walk proposition by comparing the return of professional investors against a portfolio that was chosen by throwing darts. For more information, see:

Journal's Dartboard Retires

After 14 Years of Stock Picks

By GEORGETTE JASEN

Staff Reporter of THE WALL STREET JOURNAL

Below is a graphic summarizing the results:

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Most economists believe that all three of the asset markets; stocks, bonds, and foreign exchange are quite efficient.

|This article contains a discussion among two very prominent economists from the University of Chicago about how efficient the |

|‘market’ may or may not be.. |

| |

| |[pic] |[pic][pic] |[p|

| | | |ic|

| | | |] |

| |October 18, 2004 | | |

| |

|[pi|PAGE ONE |

|c] | |

| |

[pic]Stock Characters

As Two Economists

Debate Markets,

The Tide Shifts

Belief in Efficient Valuation

Yields Ground to Role

Of Irrational Investors

Mr. Thaler Takes On Mr. Fama

By JON E. HILSENRATH

Staff Reporter of THE WALL STREET JOURNAL

October 18, 2004; Page A1

For forty years, economist Eugene Fama argued that financial markets were highly efficient in reflecting the underlying value of stocks. His long-time intellectual nemesis, Richard Thaler, a member of the "behaviorist" school of economic thought, contended that markets can veer off course when individuals make stupid decisions.

In May, 116 eminent economists and business executives gathered at the University of Chicago Graduate School of Business for a conference in Mr. Fama's honor. There, Mr. Fama surprised some in the audience. A paper he presented, co-authored with a colleague, made the case that poorly informed investors could theoretically lead the market astray. Stock prices, the paper said, could become "somewhat irrational."

Coming from the 65-year-old Mr. Fama, the intellectual father of the theory known as the "efficient-market hypothesis," it struck some as an unexpected concession. For years, efficient market theories were dominant, but here was a suggestion that the behaviorists' ideas had become mainstream.

"I guess we're all behaviorists now," Mr. Thaler, 59, recalls saying after he heard Mr. Fama's presentation.

Roger Ibbotson, a Yale University professor and founder of Ibbotson Associates Inc., an investment advisory firm, says his reaction was that Mr. Fama had "changed his thinking on the subject" and adds: "There is a shift that is taking place. People are recognizing that markets are less efficient than we thought." Mr. Fama says he has been consistent.

The shift in this long-running argument has big implications for real-life problems, ranging from the privatization of Social Security to the regulation of financial markets to the way corporate boards are run. Mr. Fama's ideas helped foster the free-market theories of the 1980s and spawned the $1 trillion index-fund industry. Mr. Thaler's theory suggests policy makers have an important role to play in guiding markets and individuals where they're prone to fail.

Take, for example, the debate about Social Security. Amid a tight election battle, President Bush has set a goal of partially privatizing Social Security by allowing younger workers to put some of their payroll taxes into private savings accounts for their retirements.

In a study of Sweden's efforts to privatize its retirement system, Mr. Thaler found that Swedish investors tended to pile into risky technology stocks and invested too heavily in domestic stocks. Investors had too many options, which limited their ability to make good decisions, Mr. Thaler concluded. He thinks U.S. reform, if it happens, should be less flexible. "If you give people 456 mutual funds to choose from, they're not going to make great choices," he says.

If markets are sometimes inefficient, and stock prices a flawed measure of value, corporate boards and management teams would have to rethink the way they compensate executives and judge their performance. Michael Jensen, a retired Harvard economist who worked on efficient-market theory earlier in his career, notes a big lesson from the 1990s was that overpriced stocks could lead executives into bad decisions, such as massive overinvestment in telecommunications during the technology boom.

Even in an efficient market, bad investments occur. But in an inefficient market where prices can be driven way out of whack, the problem is acute. The solution, Mr. Jensen says, is "a major shift in the belief systems" of corporate boards and changes in compensation that would make executives less focused on stock price movements.

Few think the swing toward the behaviorist camp will reverse the global emphasis on open economies and free markets, despite the increasing academic focus on market breakdowns. Moreover, while Mr. Fama seems to have softened his thinking over time, he says his essential views haven't changed.

A product of Milton Friedman's Chicago School of thought, which stresses the virtues of unfettered markets, Mr. Fama rose to prominence at the University of Chicago's Graduate School of Business. He's an avid tennis player, known for his disciplined style of play. Mr. Thaler, a Chicago professor whose office is on the same floor as Mr. Fama's, also plays tennis but takes riskier shots that sometimes land him in trouble. The two men have stakes in investment funds that run according to their rival economic theories.

Highbrow Insults

Neither shies from tossing about highbrow insults. Mr. Fama says behavioral economists like Mr. Thaler "haven't really established anything" in more than 20 years of research. Mr. Thaler says Mr. Fama "is the only guy on earth who doesn't think there was a bubble in Nasdaq in 2000."

In its purest form, efficient-market theory holds that markets distill new information with lightning speed and provide the best possible estimate of the underlying value of listed companies (IT’S THE FUNDAMENTALS – RECALL THE EQUATION). As a result, trying to beat the market, even in the long term, is an exercise in futility because it adjusts so quickly to new information.

Behavioral economists argue that markets are imperfect because people often stray from rational decisions. They believe this behavior creates market breakdowns and also buying opportunities for savvy investors(THIS IN A SENSE IS ARGUING THAT YOU CAN BEAT THE MARKET AT CERTAIN TIMES!) Mr. Thaler, for example, says stocks can under-react to good news because investors are wedded to old views about struggling companies.

For Messrs. Thaler and Fama, this is more than just an academic debate (WHAT DOES MORE THAN ACADEMIC MEAN??). Mr. Fama's research helped to spawn the idea of passive money management and index funds. He's a director at Dimensional Fund Advisers, a private investment management company with $56 billion in assets under management. Assuming the market can't be beaten, it invests in broad areas rather than picking individual stocks. Average annual returns over the past decade for its biggest fund -- one that invests in small, undervalued stocks -- have been about 16%, four percentage points better than the S&P 500, according to Morningstar Inc., a mutual-fund research company.

Mr. Thaler, meanwhile, is a principal at Fuller & Thaler, a fund management company with $2.4 billion under management. Its asset managers spend their time trying to pick stocks and outfox the market (TRYING TO PICK WINNERS!) The company's main growth fund, which invests in stocks that are expected to produce strong earnings growth, has delivered average annual returns of 6% since its inception in 1997, three percentage points better than the S&P 500.

Mr. Fama came to his views as an undergraduate student in the late 1950s at Tufts University when a professor hired him to work on a market-forecasting newsletter. There, he discovered that strategies designed to beat the market didn't work well in practice. By the time he enrolled at Chicago in 1960, economists were viewing individuals as rational, calculating machines whose behavior could be predicted with mathematical models. Markets distilled these differing views with unique precision, they argued.

"In an efficient market at any point in time the actual price of a security will be a good estimate of its intrinsic value," Mr. Fama wrote in a 1965 paper titled "Random Walks in Stock Market Prices." Stock movements were like "random walks" because investors could never predict what new information might arise to change a stock's price. In 1973, Princeton economist Burton Malkiel published a popularized discussion of the hypothesis, "A Random Walk Down Wall Street," which sold more than one million copies.

Mr. Fama's writings underpinned the Chicago School's faith in the functioning of markets. Its approach, which opposed government intervention in markets, helped reshape the 1980s and 1990s by encouraging policy makers to open their economies to market forces. Ronald Reagan and Margaret Thatcher ushered in an era of deregulation and later Bill Clinton declared an end to big government. After the collapse of Communist central planning in Russia and Eastern Europe, many countries embraced these ideas.

As a young assistant professor in Rochester in the mid-1970s, Mr. Thaler had his doubts about market efficiency. People, he suspected, were not nearly as rational as economists assumed.

Mr. Thaler started collecting evidence to demonstrate his point, which he published in a series of papers. One associate kept playing tennis even though he had a bad elbow because he didn't want to waste $300 on tennis club fees. Another wouldn't part with an expensive bottle of wine even though he wasn't an avid drinker. Mr. Thaler says he caught economists bingeing on cashews in his office and asking for the nuts to be taken away because they couldn't control their own appetites (THESE ARE SUPPOSEDLY EXAMPLES OF IRRATIONAL BEHAVIOR)

Mr. Thaler decided that people had systematic biases that weren't rational, such as a lack of self-control (LACK OF SELF CONTROL – THALER WANTS TO EXPLOIT THIS!!). Most economists dismissed his writings as a collection of quirky anecdotes, so Mr. Thaler decided the best approach was to debunk the most efficient market of them all -- the stock market.

Small Anomalies

Even before the late 1990s, Mr. Thaler and a growing legion of behavioral finance experts were finding small anomalies that seemed to fly in the face of efficient-market theory. For example, researchers found that value stocks, companies that appear undervalued relative to their profits or assets, tended to outperform growth stocks, ones that are perceived as likely to increase profits rapidly. If the market was efficient and impossible to beat, why would one asset class outperform another? (Mr. Fama says there's a rational explanation: Value stocks come with hidden risks and investors are rewarded for those risks with higher returns.)

Moreover, in a rational world, share prices should move only when new information hit the market. But with more than one billion shares a day changing hands on the New York Stock Exchange, the market appears overrun with traders making bets all the time.

Robert Shiller, a Yale University economist, has long argued that efficient-market theorists made one huge mistake: Just because markets are unpredictable doesn't mean they are efficient. The leap in logic, he wrote in the 1980s, was one of "the most remarkable errors in the history of economic thought." Mr. Fama says behavioral economists made the same mistake in reverse: The fact that some individuals might be irrational doesn't mean the market is inefficient (IN OTHER WORDS, AS LONG AS THE MAJORITY OF INVESTORS ARE RATIONAL THEN MARKETS WILL BE EFFICIENT – ADD IN THE FOOTBALL BETTING THESIS)

Shortly after the stock market swooned, Mr. Thaler presented a new paper at the University of Chicago's business school. Shares of handheld-device maker Palm Inc. -- which later split into two separate companies -- soared after some of its shares were sold in an initial public offering by its parent, 3Com Corp., in 2000, he noted. The market gave Palm a value nearly twice that of its parent even though 3Com still owned 94% of Palm. That in effect assigned a negative value to 3Com's other assets. Mr. Thaler titled the paper, "Can the Market Add and Subtract?" It was an unsubtle shot across Mr. Fama's bow. Mr. Fama dismissed Mr. Thaler's paper, suggesting it was just an isolated anomaly. "Is this the tip of an iceberg, or the whole iceberg?" he asked Mr. Thaler in an open discussion after the presentation, both men recall (HIGH BROW INSULT FOR SURE!!)

Mr. Thaler's views have seeped into the mainstream through the support of a number of prominent economists who have devised similar theories about how markets operate. In 2001, the American Economics Association awarded its highest honor for young economists -- the John Bates Clark Medal -- to an economist named Matthew Rabin who devised mathematical models for behavioral theories (I WONDER IF THESE MATHEMATICAL MODELS FAILED RECENTLY??) . In 2002, Daniel Kahneman won a Nobel Prize for pioneering research in the field of behavioral economics. Even Federal Reserve Chairman Alan Greenspan, a firm believer in the benefits of free markets, famously adopted the term "irrational exuberance" in 1996 (PARSE THIS TERM! RECALL THALER ARGUES THAT AT TIMES, PEOPLE EXPERIENCE LACK OF CONTROL!)

Andrew Lo, an economist at the Massachusetts Institute of Technology's Sloan School of Management, says efficient-market theory was the norm when he was a doctoral student at Harvard and MIT in the 1980s (OF COURSE IT WAS THE NORM!!! )"It was drilled into us that markets are efficient. It took me five to 10 years to change my views." In 1999, he wrote a book titled, "A Non-Random Walk Down Wall Street."

In 1991, Mr. Fama's theories seemed to soften. In a paper called "Efficient Capital Markets: II," he said that market efficiency in its most extreme form -- the idea that markets reflect all available information so that not even corporate insiders can beat it -- was "surely false." Mr. Fama's more recent paper also tips its hand to what behavioral economists have been arguing for years -- that poorly informed investors could distort stock prices.

But Mr. Fama says his views haven't changed. He says he's never believed in the pure form of the efficient-market theory. As for the recent paper, co-authored with longtime collaborator Kenneth French, it "just provides a framework" for thinking about some of the issues raised by behaviorists, he says in an e-mail. "It takes no stance on the empirical importance of these issues."

The 1990s Internet investment craze, Mr. Fama argues, wouldn't have looked so crazy if it had produced just one or two blockbuster companies, which he says was a reasonable expectation at the time. Moreover, he says, market crashes confirm a central tenet of efficient market theory -- that stock-price movements are unpredictable. Findings of other less significant anomalies, he says, have grown out of "shoddy" research.

Defending efficient markets has gotten harder, but it's probably too soon for Mr. Thaler to declare victory. He concedes that most of his retirement assets are held in index funds, the very industry that Mr. Fama's research helped to launch. And despite his research on market inefficiencies, he also concedes that "it is not easy to beat the market, and most people don't." (PUT YOUR MONEY WHERE YOUR MOUTH IS AND NO KIDDING, IT IS TOUGH TO BEAT THE MARKET!)

Write to Jon E. Hilsenrath at jon.hilsenrath@1

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Using technical analysis

Although there are many, these Bollinger Bands examples will give us a good feel for the notion of technical analysis. Note that technical analysis is completely removed from the fundamentals, which are based on expected profits and interest rates. As such, “technical analysts” are often referred to as “chart watchers,” as the following, as the following analysis demonstrates.

Bollinger bands are a very useful and popular technique in predicting stock movements. They provide many useful signals, such as whether a price is relatively high or low, whether a current trend is likely to continue or reverse, and market volatility. What separates Bollinger bands from most other price channeling techniques is in the way the bands are derived. Rather than setting the channels at a fixed percentage above and below the moving average, Bollinger bands are plotted two standard deviations above and below the moving average. This is done to ensure that 95% of price data will fall between the bands. It also ensures that the bands are sensitive to volatility.

When speaking of market trends, Bollinger bands can provide a signal based on both penetrations of the bands, as well as width of the bands. A penetration of either band, high or low, implies a continuation of the current trend. When the bands move far apart relative to the norm, the current trend may be ending. If the bands are unusually tight, it may be a sign of a new trend beginning.

Price targets can also be achieved through the use of Bollinger bands. For example, if a price is moving along the lower band and proceeds to cross above the moving average, the upper band will become a price target. Of course, the opposite also applies.

Finally, momentum can also be checked through the use of Bollinger bands. If a price is seen to move above or below a band, and on a subsequent move, fails to reach the band for a second time, there is a good chance that momentum is being lost and a reversal may be in the works. It is important to note that even if the subsequent move reaches a

higher or lower price, it must still penetrate the respective band in order to indicate lasting momentum.

Bollinger Bands – Test One

[pic]

Above we see a current six-month chart of Dell Inc. (DELL) The standard set up for use of Bollinger bands includes a six-month chart, along with a 20-day moving average. Starting from the left portion of the graph, you can see the sell signals, indicated by red arrows. As you can see, as the price bars pass through the bottom band during mid-March, a trend may be starting. In addition, the bands are fairly tight during this time period. As we progress into the early and middle of April, the lower band continues to be penetrated by the price, confirming the downtrend. As the bands widen into May, the price begins to stabilize and then rise. Dell’s price then crosses through the moving average and continues up through the upper band. However, it does not continue to hug the band, so no uptrend can be confirmed. As the bands become very wide through late May and early June, the price evens out. Two more potential buy signals are seen in June and July, but once again, only for a couple of days at a time. During this time, attention should also be focused on the bands, which are once again becoming tighter.

Looking back on what was just covered; it is safe to say that the rules regarding Bollinger bands seem to work just as described. For each change in price, the bands properly adjusted and did not provide any erratic signals. That being said, the buy and sell signals shown on the graph should not be immediately followed as soon as a band is penetrated. While each instance would provide a profit if followed, most would be minimal.

Using the rules provided by Bollinger bands, it would seem quite easy to predict the short-term future for Dell’s stock price. However, there are no definitive movements currently in progress. We can still take a look at what the chart is showing us and try to make an educated guess. The bands are beginning to widen once again, implying less volatility. The price has recently dropped below the moving average and seems to be staying somewhat near the lower band. The price drop does not appear to look

dramatically sharp, and looking at similar trends and price levels throughout the past six months, it seems as though there will be no drastic price changes in the near future. But, if the price continues to descend throughout the following week and eventually hugs the bottom band, there is a good chance we may be seeing the start of a downtrend worth moving in on with a short-position.

Bollinger Bands – Test Two

To get a better view of the accuracy and potential gains associated with Bollinger bands, let’s take a look at some more examples and see how they fare. The chart below depicts the current state of Ford Motor Company’s (F) stock. It provides a good look at a consistent downtrend beginning in late February through mid-April. Taking a short position at first sign of a downtrend on February 25 at a price of 13.00 and riding it out through April 22 at 9.89 would provide a change of 23.92%. Comparing this change to

the S&P 500 rate of 4.89%, we can undoubtedly say that we would have beaten the market. Also interesting to point out is the single buy signal, which if followed would provide a false signal, and thus a loss.

[pic]

Bollinger Bands – Test Three

The next chart shows the previous six months of International Business Machines (IBM) stock and a good opportunity to profit from both the drop and rise in price during this time. If a short position was taken at the first sell signal on March 22 at a price of 89.50 and held onto until it was clear that the trend was over on, say, April 26 at 74.65, then it would clearly show a market beating opportunity (-16.59% change). During the same time period, the S&P 500 was growing at a rate of -1.70%, so it is clear that following the bands would have paid off.

In the second part, taking a long position at the sign of an uptrend starting July 11 at a price of 78.96 and selling off on July 22 (84.44) once it appears the trend is over, another profitable opportunity is seen. A change of 6.94% is seen, as compared to the S&P 500 of 1.17%.

[pic]

Bollinger bands can provide information about the market that many other technical strategies cannot. When seeking information regarding volatility, the bands are second to none. Furthermore, once locked into a trend, Bollinger bands can give us a very good idea of what to expect in the near future. One needs to use caution when studying Bollinger bands however, as prices movements which penetrate the outer bands do not always send the correct signal. Instead, it is the movement that occurs near the outer bands that is most important, especially when the movements are consistent. That is where the real strength of Bollinger bands shines through.

Key Terms

1. Stock price determination formula.

2. The efficient market theory.

3. Autoregressive properties.

4. Technical analysis.

5. Jawboning.

6. Price to earnings ratio.

7. Earnings per share.

8. Inside information.

9. Random walk.

10. Two Crystal Balls

11. Bollinger bands

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hš::h?:¶hmWüh?:¶5? h?:¶H*[pic] h?:¶6 Suppose inflation over a year is 10% and I keep $100 in my pocket. That $100 next year would be able to purchase 10% less in real goods and services given the 10% rise in the general price level that has occurred over the year.

[2] This notion applies to bond and foreign exchange markets as well.

[3] In addition to the PV, near term expected profits have less uncertainty than expected profits well into the future, so when the expected profits change, it is the nearer term(s) of expected profits that have the most influence on the stock price.

[4] Psychology also plays a role here. How people feel, waves of optimism and pessimism certainly move stocks, and a strand of finance referred to as behavioral finance will be addressed at a later time. Needless to say, when we add psychology to the ‘equation,’ analysis becomes that much more difficult as well as less concrete in nature.

[5] In December of 1996, Alan Greenspan stated that investors were “irrationally exuberant,” implying that investors were erroneously optimistic about future profits. Another way to state the same thing is that a bubble had formed in the stock market! Alan Greenspan was heavily criticized for this comment and truly regrets saying it. The moral of the story is that we don’t know when stocks are overvalued or undervalued and thus, major figureheads should refrain from giving their personal opinion. The following statement is believed by just about everyone in finance and economics: “We never know if there is an asset market bubble until the bubble breaks.”

[6] We are holding expected earnings constant in this example.

[7] Let’s assume that your employer is okay with you being a little late or a little early and thus, as long as you are to work on time, on average, all is well.

[8] In the conduct of monetary policy, the Fed monitors over 850,000 data series.

[9] We would actually need two crystal balls, one to predict the NEWS and another to predict the (asset price) reaction to the NEWS.

[10] This statement ignores what is often referred to as the ‘equilibrium return’ in the ‘market.’ We know that the bond market and the stock market are often substitutes for investors’ funds and thus, investing in the stock market embodies a positive expected return.

[11] The proper jargon is thateconomists use econometrics to conduct empirical analysis. Keep in mind that the results from empirical analyses are often contentious since the results are often sensitive to the econometric techniques employed and/or the sample selection.

[12] You should recall the marginal propensity to consume from your principles classes and also that the value of the MPC plays a critical role in determining the “multiplier” and thus, determining, in part, the ‘power’ of monetary and fiscal policy.

[13] Most believe that the MPC in the US is quite high relative to the rest of the world with the empirical estimates somewhere around 0.9, which implies that for each $1.00 increase in disposable income, consumption will rise by 90 cents with the remaining 10 cents being saved.

[14] A very well known book regarding this topic is titled “A Random Walk Down Wall Street,” and is authored by Burton G. Malkiel.

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