ࡱ> ^q` TbjbjqPqP L::5I=000099980:4d;?j<0$A:A:A:AMBMBMBeeeedhelfl@h$kh'n6dhDIBMBDDdh00:A:Ai"R"R"RD08:A:Ae"RDe"R"R\lh^:A< "EZ9J$^*~`j0?j<^r]nN]nT^]n^MBZB@"RB4CMBMBMBdhdhQjMBMBMB?jDDDDd399000000 CHAPTER 8: INDEX MODELS PROBLEM SETS 1. The advantage of the index model, compared to the Markowitz procedure, is the vastly reduced number of estimates required. In addition, the large number of estimates required for the Markowitz procedure can result in large aggregate estimation errors when implementing the procedure. The disadvantage of the index model arises from the models assumption that return residuals are uncorrelated. This assumption will be incorrect if the index used omits a significant risk factor. 2. The trade-off entailed in departing from pure indexing in favor of an actively managed portfolio is between the probability (or the possibility) of superior performance against the certainty of additional management fees. 3. The answer to this question can be seen from the formulas for w 0 (equation 8.20) and w* (equation 8.21). Other things held equal, w 0 is smaller the greater the residual variance of a candidate asset for inclusion in the portfolio. Further, we see that regardless of beta, when w 0 decreases, so does w*. Therefore, other things equal, the greater the residual variance of an asset, the smaller its position in the optimal risky portfolio. That is, increased firm-specific risk reduces the extent to which an active investor will be willing to depart from an indexed portfolio. 4. The total risk premium equals: ( + (( market risk premium). We call alpha a nonmarket return premium because it is the portion of the return premium that is independent of market performance. The Sharpe ratio indicates that a higher alpha makes a security more desirable. Alpha, the numerator of the Sharpe ratio, is a fixed number that is not affected by the standard deviation of returns, the denominator of the Sharpe ratio. Hence, an increase in alpha increases the Sharpe ratio. Since the portfolio alpha is the portfolio-weighted average of the securities alphas, then, holding all other parameters fixed, an increase in a securitys alpha results in an increase in the portfolio Sharpe ratio. 5. a. To optimize this portfolio one would need: n = 60 estimates of means n = 60 estimates of variances  EMBED Equation.3 estimates of covariances Therefore, in total:  EMBED Equation.3 estimates In a single index model: ri ( rf =  i +  i (r M  rf ) + e i Equivalently, using excess returns: R i =  i +  i R M + e i The variance of the rate of return can be decomposed into the components: (l) The variance due to the common market factor:  EMBED Equation.3  (2) The variance due to firm specific unanticipated events:  EMBED Equation.3  In this model:  EMBED Equation.3  The number of parameter estimates is: n = 60 estimates of the mean E(ri ) n = 60 estimates of the sensitivity coefficient  i n = 60 estimates of the firm-specific variance 2(ei ) 1 estimate of the market mean E(rM ) 1 estimate of the market variance EMBED Equation.3  Therefore, in total, 182 estimates. The single index model reduces the total number of required estimates from 1,890 to 182. In general, the number of parameter estimates is reduced from:  EMBED Equation.3  6. a. The standard deviation of each individual stock is given by:  EMBED Equation.3  Since A = 0.8, B = 1.2, (eA ) = 30%, (eB ) = 40%, and M = 22%, we get: A = (0.82 222 + 302 )1/2 = 34.78% B = (1.22 222 + 402 )1/2 = 47.93% b. The expected rate of return on a portfolio is the weighted average of the expected returns of the individual securities: E(rP ) = wA E(rA ) + wB E(rB ) + wf rf E(rP ) = (0.30 13%) + (0.45 18%) + (0.25 8%) = 14% The beta of a portfolio is similarly a weighted average of the betas of the individual securities: P = wA A + wB B + wf  f P = (0.30 0.8) + (0.45 1.2) + (0.25 0.0) = 0.78 The variance of this portfolio is:  EMBED Equation.3  where EMBED Equation.3  is the systematic component and EMBED Equation.3 is the nonsystematic component. Since the residuals (ei ) are uncorrelated, the non-systematic variance is:  EMBED Equation.3  = (0.302 302 ) + (0.452 402 ) + (0.252 0) = 405 where 2(eA ) and 2(eB ) are the firm-specific (nonsystematic) variances of Stocks A and B, and 2(e f ), the nonsystematic variance of T-bills, is zero. The residual standard deviation of the portfolio is thus: (eP ) = (405)1/2 = 20.12% The total variance of the portfolio is then:  EMBED Equation.3  The total standard deviation is 26.45%. 7. a. The two figures depict the stocks security characteristic lines (SCL). Stock A has higher firm-specific risk because the deviations of the observations from the SCL are larger for Stock A than for Stock B. Deviations are measured by the vertical distance of each observation from the SCL. b. Beta is the slope of the SCL, which is the measure of systematic risk. The SCL for Stock B is steeper; hence Stock Bs systematic risk is greater. The R2 (or squared correlation coefficient) of the SCL is the ratio of the explained variance of the stocks return to total variance, and the total variance is the sum of the explained variance plus the unexplained variance (the stocks residual variance):  EMBED Equation.3  Since the explained variance for Stock B is greater than for Stock A (the explained variance is EMBED Equation.3 , which is greater since its beta is higher), and its residual variance  EMBED Equation.3  is smaller, its R2 is higher than Stock As. d. Alpha is the intercept of the SCL with the expected return axis. Stock A has a small positive alpha whereas Stock B has a negative alpha; hence, Stock As alpha is larger. e. The correlation coefficient is simply the square root of R2, so Stock Bs correlation with the market is higher. 8. a. Firm-specific risk is measured by the residual standard deviation. Thus, stock A has more firm-specific risk: 10.3% > 9.1% b. Market risk is measured by beta, the slope coefficient of the regression. A has a larger beta coefficient: 1.2 > 0.8 c. R2 measures the fraction of total variance of return explained by the market return. As R2 is larger than Bs: 0.576 > 0.436 d. Rewriting the SCL equation in terms of total return (r) rather than excess return (R):  EMBED Equation.DSMT4  The intercept is now equal to:  EMBED Equation.DSMT4  Since rf = 6%, the intercept would be:  EMBED Equation.DSMT4  9. The standard deviation of each stock can be derived from the following equation for R2:  EMBED Equation.3  EQ \f(Explained variance,Total variance)  Therefore:  EMBED Equation.3  For stock B:  EMBED Equation.3  10. The systematic risk for A is:  EMBED Equation.3  The firm-specific risk of A (the residual variance) is the difference between As total risk and its systematic risk: 980 196 = 784 The systematic risk for B is:  EMBED Equation.3  Bs firm-specific risk (residual variance) is: 4800 576 = 4224 11. The covariance between the returns of A and B is (since the residuals are assumed to be uncorrelated):  EMBED Equation.3  The correlation coefficient between the returns of A and B is:  EMBED Equation.3  12. Note that the correlation is the square root of R2: EMBED Equation.3   EMBED Equation.DSMT4  13. For portfolio P we can compute: P = [(0.62 980) + (0.42 4800) + (2 0.4 0.6 336)]1/2 = [1282.08]1/2 = 35.81% P = (0.6 0.7) + (0.4 1.2) = 0.90  EMBED Equation.3  Cov(rP,rM ) = P EMBED Equation.3 =0.90 400=360 This same result can also be attained using the covariances of the individual stocks with the market: Cov(rP,rM ) = Cov(0.6rA + 0.4rB, rM ) = 0.6 Cov(rA, rM ) + 0.4 Cov(rB,rM ) = (0.6 280) + (0.4 480) = 360 14. Note that the variance of T-bills is zero, and the covariance of T-bills with any asset is zero. Therefore, for portfolio Q:  EMBED Equation.3   EMBED Equation.3   EMBED Equation.3   EMBED Equation.3  15. a. Beta Books adjusts beta by taking the sample estimate of beta and averaging it with 1.0, using the weights of 2/3 and 1/3, as follows: adjusted beta = [(2/3) 1.24] + [(1/3) 1.0] = 1.16 If you use your current estimate of beta to be t 1 = 1.24, then t = 0.3 + (0.7 1.24) = 1.168 16. For Stock A:  EMBED Equation.DSMT4  For stock B:  EMBED Equation.DSMT4  Stock A would be a good addition to a well-diversified portfolio. A short position in Stock B may be desirable. 17. a. Alpha ()Expected excess return i = ri  [rf + i (rM  rf ) ]E(ri )  rf A = 20%  [8% + 1.3 (16%  8%)] = 1.6%20%  8% = 12%B = 18%  [8% + 1.8 (16%  8%)] =  4.4%18%  8% = 10%C = 17%  [8% + 0.7 (16%  8%)] = 3.4%17%  8% = 9%D = 12%  [8% + 1.0 (16%  8%)] =  4.0%12%  8% = 4%Stocks A and C have positive alphas, whereas stocks B and D have negative alphas. The residual variances are: (2(eA ) = 582 = 3,364 (2(eB) = 712 = 5,041 (2(eC) = 602 = 3,600 (2(eD) = 552 = 3,025 b. To construct the optimal risky portfolio, we first determine the optimal active portfolio. Using the Treynor-Black technique, we construct the active portfolio:  EQ \f(a, (2(e))  EQ \f(a / (2(e),Sa / (2(e)) A0.0004760.6142B0.0008731.1265C0.0009441.2181D0.0013221.7058Total0.0007751.0000Be unconcerned with the negative weights of the positive  stocks the entire active position will be negative, returning everything to good order. With these weights, the forecast for the active portfolio is:  = [ 0.6142 1.6] + [1.1265 ( 4.4)]  [1.2181 3.4] + [1.7058 ( 4.0)] =  16.90%  = [ 0.6142 1.3] + [1.1265 1.8] [1.2181 0.70] + [1.7058 1] = 2.08 The high beta (higher than any individual beta) results from the short positions in the relatively low beta stocks and the long positions in the relatively high beta stocks. (2(e) = [(0.6142)23364] + [1.126525041] + [(1.2181)23600] + [1.705823025] = 21,809.6 ( (e) = 147.68% The levered position in B [with high (2(e)] overcomes the diversification effect, and results in a high residual standard deviation. The optimal risky portfolio has a proportion w* in the active portfolio, computed as follows:  EMBED Equation.3  The negative position is justified for the reason stated earlier. The adjustment for beta is:  EMBED Equation.3  Since w* is negative, the result is a positive position in stocks with positive alphas and a negative position in stocks with negative alphas. The position in the index portfolio is: 1 (0.0486) = 1.0486 c. To calculate Sharpes measure for the optimal risky portfolio, we compute the information ratio for the active portfolio and Sharpes measure for the market portfolio. The information ratio for the active portfolio is computed as follows: A =  EMBED Equation.DSMT4  = 16.90/147.68 = 0.1144 A2 = 0.0131 Hence, the square of Sharpes measure (S) of the optimized risky portfolio is:  EMBED Equation.3  S = 0.3662 Compare this to the markets Sharpe measure: SM = 8/23 = 0.3478 ( A difference of: 0.0184 The only-moderate improvement in performance results from only a small position taken in the active portfolio A because of its large residual variance. d. To calculate the makeup of the complete portfolio, first compute the beta, the mean excess return and the variance of the optimal risky portfolio: P = wM + (wA A ) = 1.0486 + [( 0.0486) ( 2.08] = 0.95 E(RP) = P + PE(RM) = [( 0.0486) ( ( 16.90%)] + (0.95 8%) = 8.42%  EMBED Equation.3   EMBED Equation.3  Since A = 2.8, the optimal position in this portfolio is:  EMBED Equation.3  In contrast, with a passive strategy:  EMBED Equation.3 (A difference of: 0.0284 The final positions are (M may include some of stocks A through D): Bills1 0.5685 =43.15%M0.5685 ( l.0486 =59.61%A 0.5685 ( (0.0486) ( (0.6142) =1.70%B 0.5685 ( (0.0486) ( 1.1265 = 3.11%C 0.5685 ( (0.0486) ( (1.2181) =3.37%D 0.5685 ( (0.0486) ( 1.7058 = 4.71%(subject to rounding error)100.00% 18. a. If a manager is not allowed to sell short he will not include stocks with negative alphas in his portfolio, so he will consider only A and C: (2(e)  EQ \f(a, (2(e))  EQ \f(a / (2(e),Sa / (2(e))A1.63,3640.0004760.3352C3.43,6000.0009440.66480.0014201.0000The forecast for the active portfolio is:  = (0.3352 1.6) + (0.6648 3.4) = 2.80%  = (0.3352 1.3) + (0.6648 0.7) = 0.90 (2(e) = (0.33522 3,364) + (0.66482 3,600) = 1,969.03 (e) = 44.37% The weight in the active portfolio is:  EMBED Equation.3  Adjusting for beta:  EMBED Equation.3  The information ratio of the active portfolio is:  EMBED Equation.DSMT4  Hence, the square of Sharpes measure is:  EMBED Equation.DSMT4  Therefore: S = 0.3535 The markets Sharpe measure is: SM = 0.3478 When short sales are allowed (Problem 17), the managers Sharpe measure is higher (0.3662). The reduction in the Sharpe measure is the cost of the short sale restriction. The characteristics of the optimal risky portfolio are:  EMBED Equation.DSMT4  With A = 2.8, the optimal position in this portfolio is:  EMBED Equation.3  The final positions in each asset are: Bills1 0.5455 =45.45%M0.5455 ( (1 ( 0.0931) =49.47%A0.5455 ( 0.0931 ( 0.3352 =1.70%C0.5455 ( 0.0931 ( 0.6648 =3.38%100.00% b. The mean and variance of the optimized complete portfolios in the unconstrained and short-sales constrained cases, and for the passive strategy are: E(RC ) EMBED Equation.3 Unconstrained0.5685 8.42% = 4.790.56852 528.94 = 170.95Constrained0.5455 8.18% = 4.460.54552 535.54 = 159.36Passive0.5401 8.00% ' 5 6 7 8 9 I O _ | } ~      b c g h ӜӰӂtiiZjh?h@3OJQJUh?h:OJQJ jbh?h+OJQJ jah?h+OJQJh?h+H*OJQJhNOJQJh?h_nH*OJQJh?h_nCJH*OJQJaJh?h_nOJQJhC~3OJQJh?h+OJQJh?h:5OJQJh?h@3OJQJh?hLOJQJ '()   > ? @ v 8x1$^8`gd+^gd+#x^#`gd+ ^`gd+gd+1$gdGp  !1$gdGp`gd+NRvF8J hBF Tx1$^TgdGpTx1$^T`gd+  8xgdGp 8x1$^8gdGp & F 8x1$gdGp1$gdGp 81$^8gdGpTx1$^T`gdGpnpr  $ƻƻƻ}qcq[q[qMq[qh?hGpH*OJQJaJhNOJQJ j-h?h@3OJQJh?h@3H*OJQJh?hGpOJQJ!jgh?h@3EHOJQJU2jB h?h@3CJOJQJUVmHnHuh W5OJQJh?h@3OJQJjh?h@3OJQJU!jh?h@3EHOJQJU2jNB h?h@3CJOJQJUVmHnHu$.4nTVX~ôôo^!jh?h@3EHOJQJU2jB h?h@3CJOJQJUVmHnHu!jh?h@3EHOJQJU2jUB h?h@3CJOJQJUVmHnHujh?h@3OJQJUh W5OJQJh OJQJh?hGpH*OJQJaJhNOJQJh?h@3H*OJQJh?h@3OJQJ"`d246:>FHxzƻƻfUƻMƻh OJQJ!jc h?h@3EHOJQJU2j'B h?h@3CJOJQJUVmHnHuh?h@3H*OJQJh?h@3H*OJQJh?hNH*OJQJhNOJQJh?h@3CJEHOJQJh?h@3OJQJjh?h@3OJQJU!j h?h@3EHOJQJU2j^C h?h@3CJOJQJUVmHnHuFx`BXfJ  8xgdP  8xgdP1$gdP [1$^[gdP Tx1$^TgdP 8x1$^8gdP 8x1$^8`gd+ Tdh1$^Tgd 8x1$^8gdGp.02XZ\^lnpƾiXPDPDPDPDh?h@3H*OJQJhNOJQJ!jh?h EHOJQJU2j0B h?h CJOJQJUVmHnHuh?h OJQJjh?h OJQJUh h OJQJh?h@3OJQJh?h:OJQJh OJQJjh?h@3OJQJU!jk h?h@3EHOJQJU2jB h?h@3CJOJQJUVmHnHu  "&(.BDFTVXZ`blprx "$*,@BFH "*øhNhNOJQJh?hPOJQJhh8bOJQJhNCJOJQJh?h@3H*OJQJh?h@3H*OJQJhNOJQJh?h@3OJQJD*,246>@FHJRTV\^dfhjzBDFHTV|~պՠպu2jB h?h@3CJOJQJUVmHnHu!j}h?h@3EHOJQJU2jgB h?h@3CJOJQJUVmHnHujh?h@3OJQJUh?hPH*OJQJh?h@3OJQJhNOJQJhNhNOJQJh?h@3H*OJQJ'~^b    * , 2 6 : L N T f t v Ժԝԃrf[ff[ff[SfhNOJQJhNhNOJQJh?h@3H*OJQJ!j"hNhNEHOJQJU2j:O h?hNCJOJQJUVmHnHuh?h@3H*OJQJ!jh?h@3EHOJQJU2jB h?h@3CJOJQJUVmHnHuh?h@3OJQJjh?h@3OJQJU!jh?h@3EHOJQJU f "H""""#$#&#$$U%V%Y&q& & F 8x1$gdP81$^8`gdP d$1$gdIk 81$^8`gdP  8`gdP 8x`gdPFx1$^F`gdP Tx1$^TgdPv z ~ (!*!,!0!6!""""."4""""""""""#&#(###U%V%W%\%]%W&X&Y&Z&}rgh?h.tOJQJh?hIkOJQJh?h\MOJQJh?h:OJQJh OJQJ!jh?h@3EHOJQJU2jJ B h?h@3CJOJQJUVmHnHujh?h@3OJQJUh?h@3H*OJQJhNOJQJh?h@3H*OJQJh?h@3OJQJ(Z&m&n&o&p&&&&&&&''/'0'C'D'E'F'X'Y'u'{pVE{9h?h@3H*OJQJ!jj$hHshHsEHOJQJU2jO h?hHsCJOJQJUVmHnHuh?hHsOJQJjh?hHsOJQJUh?h@36OJQJ!jN"h?h@3EHOJQJU2jB h?h@3CJOJQJUVmHnHujh?h@3OJQJU!jh?h`6EHOJQJU'j|H h?h`6CJOJQJUVh?h@3OJQJq&u'v'%(&(((())))**u**** 8x1$^8gdA Tx1$^TgdA8x1$^8`gdy[  8Tgd1$gd81$^8`gd 8T`gdP d$1$gdIk 81$^8gdPu'v'%(&(c(d((((())))))))***u*v************꼴ꈀq`!j+hMhZEHOJQJUjgO hZOJQJUVhMOJQJjhMOJQJU!j'hZhZEHOJQJUjiO hZOJQJUVhHsOJQJjhHsOJQJUh?h:OJQJh?h\MOJQJh?h@3H*OJQJh?h@3OJQJh?hIkOJQJ!***** + +++++++j+k+m+n++++++++++̽衖{aP{{{!j2h?h@3EHOJQJU2jB h?h@3CJOJQJUVmHnHujh?h@3OJQJUh?h@3H*OJQJh?h:OJQJh?hIkOJQJ!j/hZhZEHOJQJUjO hZOJQJUVhZOJQJjhZOJQJUh W5OJQJh?h@3OJQJh?h@3H*OJQJ*++m++++++++,5,,,~x1$]^gdzx1$^`gd:1$gdIk 81$^8gdIk x1$^gdIk 8x^`gdIk 8x1$^8gdIkx1$]^`gdz d$1$gdIk 81$^8gdA++++++++++++,,1,2,3,4,,,,,,,,ƻƻƻƻkZƻRGƻh?hSOJQJhMOJQJ!j ;hMhMEHOJQJU2jO h?hMCJOJQJUVmHnHuh?h:OJQJ!jN8h?h@3EHOJQJU2jB h?h@3CJOJQJUVmHnHuh?h@3OJQJjh?h@3OJQJU!j`5h?h@3EHOJQJU2j_B h?h@3CJOJQJUVmHnHu,,, -2-3-4----.. .....D//>0 8x1$^8gdM x1$^gdIkx1$^`gdIk1$gdIk 81$^8gdIk 8x1$^8gdIk 8x^`gdIk,,,,+-,-3-4-6-8---------..... .ƻƻrƻƻXGƻ?h OJQJ!j#Eh?h@3EHOJQJU2j-B h?h@3CJOJQJUVmHnHu!jrBh?h@3EHOJQJU2jLB h?h@3CJOJQJUVmHnHuh?h OJQJh?hIkOJQJhMOJQJh?h@3OJQJjh?h@3OJQJU!j>hMhMEHOJQJU2jO h?hMCJOJQJUVmHnHu .".&.................//D/F/H/X/Z/\/⭜␈yh]RFh?h@3H*OJQJh?hSOJQJh?hOJQJ!jhJhMhMEHOJQJUjO hMOJQJUVhMOJQJjhMOJQJU!jHh?h@3EHOJQJU2j@.B h?h@3CJOJQJUVmHnHujh?h@3OJQJUh?h@3H*OJQJh?h@3OJQJh?h OJQJhh8bOJQJ\/^/v/x/z/|////////////////00"0$00020>0@0f0h0j0l0x0z0~0000000먗~ojh?h1}OJQJUh?h1}H*OJQJaJh?hSOJQJ!jOh?hIkEHOJQJU'j}H h?hIkCJOJQJUVjh?h@3OJQJUh?h@3H*OJQJhMOJQJh?h@3H*OJQJh?h@3OJQJhMCJOJQJ)>0n001#2F2G2H22223*3+3,33331$gdm^ T1$^Tgdm^  8Txgdm^1$gdBD 81$^8gdBD 8x1$^8gdBD#x1$^#`gdBD1$gdIk [1$^[gdBD x1$^gdIk00000011111111111222 2 222222!2#2$2+2,292:2G2H2J2L222wf!jh?h@3OJQJUaJh?h OJQJh?hOJQJh/CJOJQJh?hIkOJQJh W5OJQJh?h@3H*OJQJh?h@3OJQJjh?h1}OJQJU!jQh?hIkEHOJQJU'j}H h?hIkCJOJQJUVh?h1}OJQJ'2222222222222333333&3'3Ƶ󛈵n[A2j- ^C h?h@3OJQJUVaJmHnHu%j \h?h@3EHOJQJUaJ2ja ^C h?h@3OJQJUVaJmHnHu%jWh?h/EHOJQJUaJ2jO h?h/OJQJUVaJmHnHu!jh?h@3OJQJUaJ%jSh?hHEHOJQJUaJ2j ^C h?h@3OJQJUVaJmHnHuh?h@3OJQJaJ'3(3)3*3+3,3.333=3E3333333@4B4H4d4f4h444444øâzzk_zWLh?hm^OJQJh W5OJQJh?h@3H*OJQJh?h@3CJEHOJQJh/CJOJQJh/OJQJh?h@3OJQJhC~3h@3OJQJhC~3h*OJQJh?h OJQJh?hBDOJQJh?hOJQJh?h@3OJQJaJ!jh?h@3OJQJUaJ%j^h?h@3EHOJQJUaJ3d444455T56686F6Z66v$ !$1$Ifa$gdw9 $$1$Ifa$gdYIx1$^`gds 1$^gdy[ d1$^gdn 8d1$^8gdnd1$^`gdn1$gdm^ T1$^Tgdm^ & F Fx1$^F`gdm^ 4444444555L5N5P5R56686<6@6T6V6666666666Ƕ֧ꋀujbjbVIjIjVjh?hwrEHOJQJh?hwrH*OJQJhYIOJQJh?hwrOJQJh?h $OJQJh?h=OJQJh?h"_OJQJ!jeh/h/EHOJQJUjlO h/OJQJUV!jvah/h/EHOJQJUjO h/OJQJUVh/OJQJjh/OJQJUh?h@3OJQJh?h#EOJQJ6666|n $$1$Ifa$gdw9 $$1$Ifa$gdYItkdi$$Ifl0*& t04 la666666666666666776787`7b7d7777777888L8N8P8t8x8z8999999999999999999:::h?hwrH*OJQJ jsh?hwrOJQJh?hYIOJQJh?hwrEHH*OJQJh?hwrCJEHOJQJh?hwrH*OJQJh?hwrOJQJh?hwrEHOJQJhYIOJQJ966@7^7q $$1$Ifa$gdw9 $1$IfgdYItkd}j$$Ifl0*&  t04 la^7`777q $$1$Ifa$gdw9 $1$Ifgdw9tkd;@;J;Q;lU 8$1$If^8`gdw9 *T$1$If^T`gdw9$ 8$1$If^8`a$gdw9akdo$$IfTP4FP`    4 Paf4TQ;R;X;b;i;lU 8$1$If^8`gdw9 *T$1$If^T`gdw9$ 8$1$If^8`a$gdw9akdp$$IfTP4FP`    4 Paf4Ti;j;<<2===B>>qaUI 8d1$^8gdS: 8d1$^8gdYIhd1$^h`gdYIhd1$^h`gdA 8d^`gdV(  8xgdnakd\q$$IfTP4FP`    4 Paf4T<<<<(<6<<<<2=4=L=N=n=p==========>>>>$>%>6>7>>>>>??????+?,?-??D?G?R?S?W?ϿϬϒϒϒϒϬτ jsh?hAOJQJh?hwrH*OJQJ jsh?hwrOJQJhAOJQJh?hYIOJQJh{jOJQJhYIOJQJh?hwrOJQJhV(OJQJhwrOJQJhV(hwrOJQJhV(hV(OJQJ4>D?R?b?F@^@@@@AABBB,CDC 8Td`gdS:8d1$]^8`gdS: T1$^Tgd  8dgdS: Td1$^TgdS:Z8d1$]Z^8gdS: d1$`gdA 8d1$^8gdS: d1$]gdAW?b?c????@@F@G@Z@[@\@]@@@@@@@@@AApVEp=hROJQJ!j!wh?hwrEHOJQJU2j0A h?hwrCJOJQJUVmHnHu!jh?hwrEHOJQJUh?hJOJQJ!j rhAhAEHOJQJU2jO h?hACJOJQJUVmHnHujh?hwrOJQJUh?hwrEHOJQJh?hwrH*OJQJ jsh?hwrOJQJhV(OJQJh?hwrOJQJAABBBBBBBBB,C-C@CACBCCC}C~CCCCCCCCCCǶpd\N\FF\hnOJQJ jhV(hV(OJQJhV(OJQJh?hwrH*OJQJ!j}h?hwrEHOJQJU2jOA h?hwrCJOJQJUVmHnHujh?hwrOJQJUh?hwrH*OJQJ!j=zhAhAEHOJQJUjO hAOJQJUVhAOJQJjhAOJQJUh?hwrOJQJh?hzOJQJDCOC|CCDDE(FFFGGGH1HuH 8Tx`gdn Tx1$^Tgdn Tx1$^Tgd 8Tx`gd8x1$^8`gd1$gdD  8`gdD Tx1$^TgdV( 8x1$^8gd [1$^[gdS:CCCCE,EREtEEEEEEEEEEEEEEE F F.F0F8F:FL@LBL\L^L`LbLLLLLLLMMBMDMFMHMrMtMM蟎}ph?hwrEHOJQJ!jh?hwrEHOJQJU!j-h?hwrEHOJQJU2jĸcC h?hwrCJOJQJUVmHnHuh+CJOJQJh+OJQJjh?hwrOJQJU jsh?hwrOJQJh?hwrOJQJh?hwrH*OJQJ(`JJJJJJJJdSSSSS$dh$1$Ifa$gdw9kd$$IfTP4r` `4 Paf4T$$1$Ifa$gdw9JJJJJKKtfffff $$1$Ifa$gdw9kd$$IfTP4r` `4 Paf4TKKKKK,K:Ktfffff $$1$Ifa$gdw9kd$$IfTP4r` `4 Paf4T:KLLLMJMr`SSSSFS 8dh1$^8gd Tdh1$^Tgd 8Txx`gdkd}$$IfTP4r` `4 Paf4TJMrMMNNINeN{NNSOOOOO!P'P4P $$1$Ifa$gdw9 $1$Ifgdw9 Tx1$^Tgd $ 8Tx`gdRz 8Tx`gd $ 8Tdh`gd Tdh1$^Tgd 8dh1$^8gdMMMMNNNNNNINJNaNbNcNdNNNNNNOĹyqbQyE:qh?h0OJQJh?hwrH*OJQJ!jGh`h`EHOJQJUj;O h`OJQJUVh`OJQJjh`OJQJU!jLh+h+EHOJQJUj O h+OJQJUVh+OJQJjh+OJQJUh?hwrOJQJ!jh?hwrEHOJQJU!j@h?hwrEHOJQJU2jacC h?hwrCJOJQJUVmHnHuOOOOOOOOOOOOOEPFPJPKPgPhPpPqPPPPPNQPQRQSQfQ칪qcqqqqWh?hwrH*OJQJ j-h?hwrOJQJ jh?hwrOJQJ!jh?hwrEHOJQJU2jcC h?hwrCJOJQJUVmHnHujh?hwrOJQJUh?hwrOJQJ!jMh8h8EHOJQJUjO h8OJQJUVh`OJQJjh`OJQJUhMOJQJ4P;PPVP]Pi^PA N$1$Ifgdw9 $$1$Ifa$gdw9 $1$Ifgdw9kd$$IflF>2f` 4 t0    4 laJ !N$1$Ifgdw9]P^P`P{PPzoaR N$1$Ifgdw9 $$1$Ifa$gdw9 $1$Ifgdw9kd֪$$IflF>2f` 4 t0    4 laJPPPPPzoaR N$1$Ifgdw9 $$1$Ifa$gdw9 $1$Ifgdw9kd$$IflF>2f` 4 t0    4 laJPPPPPzoaR N$1$Ifgdw9 $$1$Ifa$gdw9 $1$Ifgdw9kdP$$IflF>2f` 4 t0    4 laJPPPJQKQRQjQzoXM?? $$1$Ifa$gdw9 $1$Ifgdw9 TEFx]E^F`gd.D  !1$gd $kd$$IflF>2f` 4 t0    4 laJfQgQhQiQQQQQQQQQQQQQQQQQQQQQ\]pqrsƻƻpƻ!jh?hwrEHOJQJU2jtdC h?hwrCJOJQJUVmHnHuUh?hwrH*OJQJhuOJQJhuCJOJQJh?hwrOJQJjh?hwrOJQJU!jh?hwrEHOJQJU2jvudC h?hwrCJOJQJUVmHnHu,jQkQyQQQuj_j $1$Ifgdu $1$Ifgdw9kd$$IflF.  P   t0    4 laJQQQQQujjj $1$Ifgdw9kd$$IflF.  P  t0    4 laJQQQ"ujjj $1$Ifgdw9kd$$IflF.  P  t0    4 laJ = 4.320.54012 529.00 = 154.31The utility levels below are computed using the formula:  EMBED Equation.3  Unconstrained 8% + 4.79% (0.005 2.8 170.95) = 10.40% Constrained 8% + 4.46% (0.005 2.8 159.36) = 10.23% Passive 8% + 4.32% (0.005 2.8 154.31) = 10.16% 19. All alphas are reduced to 0.3 times their values in the original case. Therefore, the relative weights of each security in the active portfolio are unchanged, but the alpha of the active portfolio is only 0.3 times its previous value: 0.3 (16.90% = (5.07% The investor will take a smaller position in the active portfolio. The optimal risky portfolio has a proportion w* in the active portfolio as follows:  EMBED Equation.3  The negative position is justified for the reason given earlier. The adjustment for beta is:  EMBED Equation.3  Since w* is negative, the result is a positive position in stocks with positive alphas and a negative position in stocks with negative alphas. The position in the index portfolio is: 1 (0.0151) = 1.0151 To calculate Sharpes measure for the optimal risky portfolio we compute the information ratio for the active portfolio and Sharpes measure for the market portfolio. The information ratio of the active portfolio is 0.3 times its previous value: A =  EMBED Equation.DSMT4 = 0.0343 and A2 =0.00118 Hence, the square of Sharpes measure of the optimized risky portfolio is: S2 = S2M + A2 = (8%/23%)2 + 0.00118 = 0.1222 S = 0.3495 Compare this to the markets Sharpe measure: SM =  EMBED Equation.DSMT4 = 0.3478 The difference is: 0.0017 Note that the reduction of the forecast alphas by a factor of 0.3 reduced the squared information ratio and the improvement in the squared Sharpe ratio by a factor of: 0.32 = 0.09 20. If each of the alpha forecasts is doubled, then the alpha of the active portfolio will also double. Other things equal, the information ratio (IR) of the active portfolio also doubles. The square of the Sharpe ratio for the optimized portfolio (S-square) equals the square of the Sharpe ratio for the market index (SM-square) plus the square of the information ratio. Since the information ratio has doubled, its square quadruples. Therefore: S-square = SM-square + (4 IR) Compared to the previous S-square, the difference is: 3IR Now you can embark on the calculations to verify this result. CFA PROBLEMS 1. The regression results provide quantitative measures of return and risk based on monthly returns over the five-year period.  for ABC was 0.60, considerably less than the average stock s  of 1.0. This indicates that, when the S&P 500 rose or fell by 1 percentage point, ABC s return on average rose or fell by only 0.60 percentage point. Therefore, ABC s systematic risk (or market risk) was low relative to the typical value for stocks. ABCs alpha (the intercept of the regression) was 3.2%, indicating that when the market return was 0%, the average return on ABC was 3.2%. ABCs unsystematic risk (or residual risk), as measured by (e), was 13.02%. For ABC, R2 was 0.35, indicating closeness of fit to the linear regression greater than the value for a typical stock.  for XYZ was somewhat higher, at 0.97, indicating XYZ s return pattern was very similar to the  for the market index. Therefore, XYZ stock had average systematic risk for the period examined. Alpha for XYZ was positive and quite large, indicating a return of 7.3%, on average, for XYZ independent of market return. Residual risk was 21.45%, half again as much as ABCs, indicating a wider scatter of observations around the regression line for XYZ. Correspondingly, the fit of the regression model was considerably less than that of ABC, consistent with an R2 of only 0.17. The effects of including one or the other of these stocks in a diversified portfolio may be quite different. If it can be assumed that both stocks betas will remain stable over time, then there is a large difference in systematic risk level. The betas obtained from the two brokerage houses may help the analyst draw inferences for the future. The three estimates of ABCs "#tucSSE R1$^ `Rgd $ Rx1$^ `Rgd $8xx1$]^8gd $kdD$$IflF.  P  t0    4 laJ  "2p!j]huh{jEHOJQJU2jO h?h{jCJOJQJUVmHnHujh?hwrOJQJUh?hwrEHOJQJ j-h?hwrOJQJh?h$OJQJh?hOJQJh&OJQJhuCJOJQJhuOJQJh?hwrOJQJ'%2JJ#= 81$^8gd d1$^gdd1$]^gd d1$^gd& 8d^`gd 8d1$^8gd #d1$^#gdd1$^`gd$23FGHI-./0?@wǶtcWWWKWh?hwrH*OJQJh?hwrH*OJQJ!jhuhuEHOJQJUjO huOJQJUVhuOJQJjhuOJQJUh?hwr6OJQJh&OJQJh?hwrOJQJ!jkh?hwrEHOJQJU2jdC h?hwrCJOJQJUVmHnHuh?hwrEHOJQJ!jh?hwrEHOJQJU  "'HYtu힓}rg}r}g}r}r}r}r}r}rgr}rh?hOJQJh?hOOJQJh?h_nOJQJh?hDuOJQJh?hsOJQJh?h@3OJQJ!jLhuhuEHOJQJUjO huOJQJUVjhuOJQJUh?hwrH*OJQJh?hwrH*OJQJh?hwrOJQJhuOJQJ(N\]^VXZ#x1$^#`gds1$gds#1$]^#gds #x1$^#gdsx1$^`gds1$gds 1$^gd& 1$^gd1$^`gd_n d$1$gd&,-Vgt &*79BMNO[\^_~pq:<÷uh?hsH*OJQJh?hsCJOJQJhuOJQJh?h"_OJQJh?hsOJQJh&hsOJQJh?hs5OJQJhh8b5OJQJh&OJQJh?h_nOJQJh?h3OJQJh?hOOJQJh?hOJQJ.(*xzZ\^lnpr팈hh8hJN5jhJN5Uh?h_nOJQJ jh?hsOJQJ j-h?hsOJQJ jbh?hsOJQJh?h"_OJQJh?h3OJQJUh?hsH*OJQJh?hsOJQJhuOJQJ. are similar, regardless of the sample period of the underlying data. The range of these estimates is 0.60 to 0.71, well below the market average  of 1.0. The three estimates of XYZ s  vary significantly among the three sources, ranging as high as 1.45 for the weekly data over the most recent two years. One could infer that XYZ s  for the future might be well above 1.0, meaning it might have somewhat greater systematic risk than was implied by the monthly regression for the five-year period. These stocks appear to have significantly different systematic risk characteristics. If these stocks are added to a diversified portfolio, XYZ will add more to total volatility. 2. The R2 of the regression is: 0.702 = 0.49 Therefore, 51% of total variance is unexplained by the market; this is nonsystematic risk. 3. 9 = 3 + ( (11 ( 3) ( ( = 0.75 4. d. 5. b.     CHAPTER 8: INDEX MODELS 8- PAGE 10 lnp "$1$gd $1$^`gds d$1$gd_n1$]^gd3 "$&*,8:>@BDFHJLNRTŴŧ矣h?hsOJQJhJN5h@3h8h@3CJOJQJ!hR0JCJOJQJmHnHu%jh8hh8b0JCJOJQJUh8hh8b0JCJOJQJhh8h]hh8bhh8bCJOJQJ$&BDFHJLNPRT1$gd $gdh8b$a$gdh8b J 000PP:ph8b>0@PBP/ =!"#$% gDd B  S A? 26`Z#_v19(D`!6`Z#_v19( @ dsxR=H@~IX0Cppbः n-*Vh!tsڱKvUpPwnOj ^ݽ! `?LYJ!jDZD8 N 3r)F$A,a~{?pcpf_2DKqϣҞ$flt"P8o[~n7jn5|4.5QEO5=C[^7/h~k\s)je]P\9t:Ct 7c*'r'59kT\$8?tèpUg뻶{j/Ғ]D N>4c`/Ȝ{`Dd +B  S A? 2GX0z$/u`!GX0z$/u Mdlxcdd``d 2 ĜL0##0KQ*faR`y)d3H1icY+xʓ@=P5< %!@5 @_L ĺE,a  ſATN`gbM-VK-WMcXBW\% \P3A~g0ZtA*Td%Bg>71ryp~3o G1@!.VOrE Lb.;#XB +ss>/] 4)$JCb.̿1 #l7Wے g\x;b;+KRs7u3t106viDd XhB + S A+? 2sKz|&f6_ !`!WsKz|&f6@|%xUPJ@};i !x/ JR{M$xAz⡟V<I.ü3of l- H )*BоڨE&[cM ! g|raiz2:E4+! $<:YШqg/oF0n/L=_,Ub W&00z)$FFL@FWrAC `CPF&&\Ϭiy ] A4'f~`ZDd D|B - S A-? 2Z]dkRM !`!Z]dkR `0fxcdd``fd``baV d,FYzP1C&,7\Sn! KA?HZ l@P5< %! `Wfjv L@(\p+ciu@|!}9T T+@Z+a|MN? ?̎ʟVBWd? br<?#gxvGV%τ}YQw1C䱄^w!9 `N=pc|=0_wcFkJN(߄r/K#8Ƣ;:+KRsʣY:A.06z(20L۳фdDq%7\` ;FLLJ% OXBAh] `! K}Dd 4B  S A? 2&I@*zER `!&I@*zERR X`\x;KAg.s9|"G QDc-|*0F1, L ւB: AV*;{k"2HU_4b|&01e1 PXG}h7L[V;BH2p9׸Uș\|_(L>_(4#0UX]:QuL#ӹM%o_Xsɱ2b2v g$Ӛk[3j{ABq2_z<OsKvf43ۘܗ{+퟊Q/3DSA~eWs} kw!.Td 6~Jm^vKkd!  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~>68Root Entry F,KEZData ]WordDocumentLObjectPool>EZ,KEZ_1122294862F>EZEZOle CompObjfObjInfo !&)*-01478;>ADGJKLMNOPQTWX[^_`cfilmnoruvwxyz{| FMicrosoft Equation 3.0 DS Equation Equation.39qiH`\! n 2" n2=1,770 FMicrosoft Equation 3.0 DS EqEquation Native d_1122294994 FEZEZOle CompObj fuation Equation.39qiL n 2 +3n2=1,890 FMicrosoft Equation 3.0 DS Equation Equation.39qObjInfo Equation Native  h_1122295637FEZEZOle  CompObj fObjInfoEquation Native R_1122295769 "FEZEZi6p  i2  M2 FMicrosoft Equation 3.0 DS Equation Equation.39qi5Ȃ'  2 (e i )Ole CompObjfObjInfoEquation Native Q_1130241931,wFEZEZOle CompObjfObjInfo FMicrosoft Equation 3.0 DS Equation Equation.39q*}@ Cov(r i ,r j )= i  j Equation Native _1122296103FEZEZOle CompObj f FMicrosoft Equation 3.0 DS Equation Equation.39qi@\!  M2 FMicrosoft Equation 3.0 DS Equation Equation.39qObjInfo!"Equation Native #;_1122296447'$FEZEZOle $CompObj#%%fObjInfo&'Equation Native (_1122303792)FEZEZik\! n 2 +3n2() to (3n+2) FMicrosoft Equation 3.0 DS Equation Equation.39qi\!  i =[Ole +CompObj(*,fObjInfo+.Equation Native / i2  M2 + 2 (e i )] 1/2 FMicrosoft Equation 3.0 DS Equation Equation.39qi\!  P2 = P2  M2 + 2_1122304871J.FEZEZOle 2CompObj-/3fObjInfo05Equation Native 6_11223050003FEZEZOle 9CompObj24:f (e P ) FMicrosoft Equation 3.0 DS Equation Equation.39qi6   P2  M2ObjInfo5<Equation Native =R_11223050491@8FEZEZOle ?CompObj79@fObjInfo:BEquation Native CQ_1335687994r=FEZEZ FMicrosoft Equation 3.0 DS Equation Equation.39qi5C{  2 (e P ) FMathType 6.0 Equation MathType EFEquation.DSMT49qOle ECompObj<>FiObjInfo?HEquation Native I< 9TDSMT6WinAllBasicCodePagesTimes New RomanSymbolCourierPSMT Extra!/'_!!/G_APAPAE%B_AC_A %!AHA_D_E_E_A  s 2 (e P )==w A2 s 2 (e A )++w B2 s 2 (e B )++w f2 s 2 (e f ) FMicrosoft Equation 3.0 DS Equation Equation.39qi\!  P2 =(0.78 2 22 2 )_1122307146BFEZEZOle RCompObjACSfObjInfoDUEquation Native V_1216126905GFEZEZOle YCompObjFHZf+405=699.47 FMicrosoft Equation 3.0 DS Equation Equation.39qc`d Times New RomanR 2 = i2  M2  i2  M2 + ObjInfoI\Equation Native ]_11223078186|LFEZEZOle a2 (e i ) FMicrosoft Equation 3.0 DS Equation Equation.39qi6\!  B2  M2CompObjKMbfObjInfoNdEquation Native eR_1341061344QF EZ EZOle gCompObjPRhiObjInfoSjEquation Native k FMathType 6.0 Equation MathType EFEquation.DSMT49q9TDSMT6WinAllBasicCodePagesTimes New RomanSymbolCourierPSMT Extra!/'_!!/G_APAPAE%B_AC_A %!AHA_D_E_E_A  s 2 (e B )_1341061481^VF EZ EZOle pCompObjUWqiObjInfoXs FMathType 6.0 Equation MathType EFEquation.DSMT49q9TDSMT6WinAllBasicCodePagesTimes New RomanSymbolCourierPSMT Extra!/'_!!/G_APAPAE%B_AC_A %!AHA_D_E_E_A  r A "-rEquation Native t_1341061735[F EZ EZOle }CompObjZ\~i f ==a++b(r M "-r f )!r A ==a++r f (1"-b)++br M FMathType 6.0 Equation MathType EFEquation.DSMT49qObjInfo]Equation Native x_1341061818Y`F EZ EZOle \9TDSMT6WinAllBasicCodePagesTimes New RomanSymbolCourierPSMT Extra!/'_!!/G_APAPAE%B_AC_A %!AHA_D_E_E_A  a++r f (1"-b)==1%++r f (1"-1.2)CompObj_aiObjInfobEquation Native e_1122308824eF EZ EZ FMathType 6.0 Equation MathType EFEquation.DSMT49qI9TDSMT6WinAllBasicCodePagesTimes New RomanSymbolCourierPSMT Extra!/'_!!/G_APAPAE%B_AC_A %!AHA_D_E_E_A  1%++6%(1"-1.2)==1%"-1.2%=="-0.2% FMicrosoft Equation 3.0 DS Equation Equation.39qiv@\! R i2 = i2  M2  i2 =Ole CompObjdffObjInfogEquation Native _1122308959cmjF EZ EZOle CompObjikfObjInfol FMicrosoft Equation 3.0 DS Equation Equation.39qi̛  A2 = A2  M2 R A2 =0.7 2 20 2 0.20=980 AEquation Native #_1122309009oF EZ EZOle CompObjnpf =31.30% FMicrosoft Equation 3.0 DS Equation Equation.39qiCS  B2 =1.2 2 20 2 0.12=4,800 B =ObjInfoqEquation Native _1335688343tF EZ EZOle 69.28% FMathType 6.0 Equation MathType EFEquation.DSMT49qf9TDSMT6WinAllBasicCodePagesTimes New RomanSymbolCourierPSMT Extra!/'_!!/G_APAPAE%B_AC_A %!AHA_D_E_E_ACompObjsuiObjInfovEquation Native _1335688354yF EZ EZ  b A2 s M2 ==0.70 2 20 2 ==196 FMathType 6.0 Equation MathType EFEquation.DSMT49qOle CompObjxziObjInfo{Equation Native f9TDSMT6WinAllBasicCodePagesTimes New RomanSymbolCourierPSMT Extra!/'_!!/G_APAPAE%B_AC_A %!AHA_D_E_E_A  b B2 s M2 ==1.20 2 20 2 ==576_1122310732h~F EZ EZOle CompObj}fObjInfo FMicrosoft Equation 3.0 DS Equation Equation.39qiЛ\! Cov(r A ,r B )= A  B  M2 =0.701.20400=336Equation Native _1122381285F EZ EZOle CompObjf FMicrosoft Equation 3.0 DS Equation Equation.39q-\!  AB =Cov(r A ,r B ) A  B =33631.3069.28=0.155ObjInfoEquation Native _1122381376F EZ EZOle  FMicrosoft Equation 3.0 DS Equation Equation.39q-*`\! = R 2 FMathType 6.0 Equation MathTyCompObjfObjInfoEquation Native F_1335688387F EZ EZOle CompObjiObjInfoEquation Native pe EFEquation.DSMT49q,9TDSMT6WinAllBasicCodePagesTimes New RomanSymbolCourierPSMT Extra!/'_!!/G_APAPAE%B_AC_A %!AHA_D_E_E_A  Cov(r A, r M )==rs A s M ==0.20 1/2 31.3020==280Cov(r B, r M )==rs B s M ==0.12 1/2 69.2820==480 FMicrosoft Equation 3.0 DS Eq_1216213942;F EZiEZOle CompObjfObjInfouation Equation.39qG d Times New Roman 2 (e P )= P2 " P2  M2 =1282.08"(0.90 2 400)=958.08Equation Native '_1216213961FiEZiEZOle CompObjf FMicrosoft Equation 3.0 DS Equation Equation.39qG2x Times New Roman M2 FMicrosoft Equation 3.0 DS Equation Equation.39qObjInfoEquation Native N_1130236314FiEZiEZOle CompObjfObjInfoEquation Native S_1335688617FiEZiEZ*7  Q =w P2  P2 +w M2  M2 +2w P w M Cov(r P ,r M )[] 1/2 =(0.5 2 1,282.08)+(0.3 2 40      #&'()*+,-03456789:=@ABCDEFGHKNOPQTWXYZ]`abehijkloruxy|0)+(20.50.3360)[] 1/2 =21.55% FMathType 6.0 Equation MathType EFEquation.DSMT49q9TDSMT6WinAllBasicCodePagesOle CompObjiObjInfoEquation Native  Times New RomanSymbolCourierPSMT Extra!/'_!!/G_APAPAE%B_AC_A %!AHA_D_E_E_A  b Q ==w P b P ++w M b M ==(0.50.90)++(0.31)++(0.200)==0.75_1130236769FiEZiEZOle CompObjfObjInfo FMicrosoft Equation 3.0 DS Equation Equation.39q*  2 (e Q )= Q2 " Q2  M2 =464.52"(0.75 2 400)=23Equation Native _1130236973FiEZiEZOle CompObjf9.52 FMicrosoft Equation 3.0 DS Equation Equation.39q* Cov(r Q ,r M )= Q  M2 =0.75400=300ObjInfoEquation Native _1335688709FiEZiEZOle ! FMathType 6.0 Equation MathType EFEquation.DSMT49qD9TDSMT6WinAllBasicCodePagesTimes New RomanSymbolCourierPSMT Extra!/'_!!/G_APAPAE%B_AC_A %!AHA_D_E_E_ACompObj"iObjInfo$Equation Native %2_1335688812FiEZiEZ  a A ==r A "-[r f ++b A (r M "-r f )]==.11"-[.06++0.8(.12"-.06)]==0.2% FMathType 6.0 Equation MathTyOle .CompObj/iObjInfo1Equation Native 2.pe EFEquation.DSMT49q<9TDSMT6WinAllBasicCodePagesTimes New RomanSymbolCourierPSMT Extra!/'_!!/G_APAPAE%B_AC_A %!AHA_D_E_E_A  a B ==r B "-[r f ++b B (r M "-r f )]==.14"-[.06++1.5(.12"-.06)]=="-1% FMathType 6.0 Equation MathType EFEquation.DSMT49qId9TDSMT6WinAllBasicCodePages_1335690912FiEZiEZOle ;CompObj<iObjInfo>Equation Native ?e_1098885680FiEZiEZOle ICompObjJfTimes New RomanSymbolCourierPSMT Extra!/'_!!/G_APAPAE%B_AC_A %!AHA_D_E_E_A  w 0 == a/s 2 (e)[E(r M )"-r f ]/s M2 == "-.1690/21,809.6.08/23 2 =="-0.05124 FMicrosoft Equation 3.0 DS Equation Equation.39q\! w*=w 0 1+(1")w 0 ="0.051241+(1"2.ObjInfoLEquation Native M_1335690985FiEZiEZOle R08)("0.05124)="0.0486 FMathType 6.0 Equation MathType EFEquation.DSMT49q|9TDSMT6WinAllBasicCodePagesTimes New RomanSymbolCourierPSMT Extra!/'_!!/G_APCompObjSiObjInfoUEquation Native V_1098888527FiEZiEZAPAE%B_AC_A %!AHA_D_E_E_A   as(e) FMicrosoft Equation 3.0 DS Equation Equation.39qȂ\! S 2 =SOle [CompObj\fObjInfo^Equation Native _ M2 +A 2 =823() 2 +0.0131=0.1341 FMicrosoft Equation 3.0 DS Equation Equation.39q=p\!  P2 =      !"#$%&'()*+,-./012345_79:;<=?@BACDEFGHIJKLOMNQPRSTVUXWYZ[\]`abcdefghijklmnopqrstuvwxyz{|}~߉݋6wDd  hB  S A? 2'0jPVd8J`!'0jPVd8@`z|xK@ǿwM5Bq(4 *bIb[Vh!f+" 8;. vp\Sq0q=A bNТIkLr4UA;:έl| DLܺ;? |tcPK lH_4I18@0KάNfլy9}= [I~ZO#"rCK^Qb zPpT<ʠ>ڰHjBgA}D}Uy_(|ĕbKlLV/6]z\CϽh}D8N+ZB })uTrg09I]HHG(+݄3N =mN~GbDd hB  S A? 2^iyOŸ`!^iyOŸ @|nxJ@ƿ4i <AQDR(_Rb-4VH!͋z+W^<>/ z<MmŃY_ffgaӦ"RQds-ʼE.8Zf0X$1G)iZgpԊ؈MF0n/.=_,Ub W&00n)$CFL@FWrAC `CPF&&\rC4>v.F F3X?^Dd 8h  s *A? ?3"`?2*zO6٘wf`!zO6٘wp/hxMhAtIbv#k[A/ܤD -ĸn5VTҞ<Co ^<xzEd]QM:}{H|DΤ*5 [7_⵾n|A P"p'X1*ta!P' _Y#:Y$Kƥv;t눐m'\(](~ͬlnZBߪ G-= 5kj@=l~0W^ўfYz\֖m0b|>d[|SZmgVklV݇5J\m溎 䊦sDw#{h3׃;5 bVYp2ƴ7{ZvX>h#xΈ_gEnT*VRFHmG+d4--J? `31D(ni d} E[TDxc%@c}~cG(O #DE([FUO4;ՏkP׊m)R,Tvyc{xEp7% o_= q E7!\NsQxO8! r?&{>6e87~~]濓y"}".<Շ[ty%Y4"*| jG@AXaB1< r( \ Dd lhB 3 S A3? 2|fEFJ[b"`!Z|fEFJ[@|(xcdd``~ @c112BYL%bL0Yn&B@?6 030|j䆪aM,,He`7c&,``abM-VK-WMcXBr-f \ ,@u@@ڈ 1ی*!|&߷&/ʈ*;UBod? W&00gZh7~a?#wƃ`s+a| ? {.p ;LLJ% /YbAhw݌ `LQ@RDd |h 4 s *A4? ?3"`?2;ZEmgZPŇr$`!j;ZEmgZPŇ`(+08xS;Q$`, NpPx]"D-&Vilme_?@ƱQ033K0N ,ҖBԷmS-NA\BnI$NX QO8ZW@@=ގT{-q5 8CiP|>\fcVCNûOk[TMx9Ss=Ԟ7/{-=~PY.ïe]-ɳ<.bI>;CX=fH1CTvDŽfu@7Qu[c28LcƘBA7xctjVllu bjvܵ;Vo8vн* 'HZ WHG5doAܺ967oԭzΪx'w$sWN6 dM1Wz㟕LbhH^F:@E^|'gA%\Qi' ߗsgȿfR8B>#;jc+??T|'2(Dd , b   c $A ? ?3"`?2rZL';8ʝejN(`!FZL';8ʝej `\xUMlA~3vKԨ%HzĄ薶ą.O4OJ1^ڃ7zѣc&bzi<Q|ˏ4}a77{  B$.J89Bժ΍",$| +‚_Z\B9vka[kM/ܐVu9[8RsR@]eRJ=ZzK:mxP[KW0zY'Q"wS%H:HFiUv0mK?d%bD5+SThHIrU:zyQGEzDvozlXBXGJUf'v{Uk)ѻS=DontAgDo;ь3r{ͳ¼ 2 \ѽV߶ 9G Rs%tL=*ͦcc`"`6O@i9Tr/3y5vSSZ&_f1PX*#s9~&"+6`Ai+lVnaaED(h+(LE5i% Le2M'1.CJDd \ |b   c $A ? ?3"`? 2"+P4MޟC(,`!"+P4MޟC``"!0xSoAf]HV.5證Ƙ,[\*I*xiDӃxOPo&zz2)Kc63fA@II@=K!3!{mS}N;|2's!/<~2UboEZwh<9q!"1{4PD8@X2 sMY)ey}u®E*;q^ӱt,A#JWtpѝgswH*Fr۶k7ʀ Z{;b yMqVӽ\6"Kf\Yԩa\GQڄ]:GAb֊S8Y{*o!#V'%j=u%K4ŕr޼]/p xr4;0QPmk,~6Y7vgOl*#~YDd @b   c $A ? ?3"`? 2y1#_[ݨt/`!wy1#_[ݨtj$ ExuRkQvmȦMa%&mr^"I""lb\@~x*9 oқ Qo<$$Rgwvf73;of-)wKՄL&gآb~Ir^u ?~"* ]!diGNa$k˲"4< z΅pqZ޴lﴛ>{֯} <4Um@&} N)c='7xD/刮 }#ЈƐ`+SIʼ{T7D4OCIiڼТ4};Vbs8I4'nS=gxcxa>w[ntqk}`5=5N;d:u/YqDd B ! S A!?  2u_Mн,33!`!u_Mн,@ }x}RJ@l6,AC'ۃ UmXŐ[o',豂 ؃Q0nb*;7v 2FL S FӈaͱqmPb?GN $݊M=Y(VJALe3 fO|dœ+^pf+{/>q[dVEҥ@'oi~ kAEW~0SixnYw}2?(~kƸuN_HR8GŋqƏyRƚ,{s&΁qR[q[ TX=bSv= C 5¿{fH7tDd D 8B  S A? 2X>@Z}-n45!`!,>@Z}-nkv xOA{?ܽ[ѡ|6)Tav|" i?|GP=Ht(8h'4mmq?ivF5AZGY1\\:g; Pl5saQ"=9 d4u/tSVxj_qG8'/s\Yk9]"o)0SnO~8!`!%>)0SnO~`@ x1KQgfwޡǩ bqbc6jĻxrN S hgTiADk df*)77 x7~\=<! )c*8n֪dTQ KښR01ˠd ֘=X\_C6{J GiFV) VkD?oqoL}ҧ=]ڜ1{»hk.A2S`vyj3>('aIf wiPե=Pq\þ+L[IVʑ~^V@WycT\\N,s'pU}w}ӣ؋G'^ z9Cgk?Ω#?ԕDd |h $ s *A$? ?3"`?2kgwT  O;!`!kgwT  ` 0xSkA~3D$bۍMZ MJ4i@n$Vj"HzPZ^<דHHvfgoCHbJ!:;!co/ j؏%_d䫏ehv mMcNz89i]q_RC|\([,vǬi*|Qcj?kׇLF}Alc׼U)\-b1yX}v"Ţxl|jߤl.f ؊C]lP7(UK%7_zQQykW%n\JaXv<[!rfD#l{^) % //[ƍdR5bYf`^n Q f3Fv~/-b!YyhEaow+,aoxh3Y-G+]n"9=v_P';e_7gr؅IZ# [X~{l.e2 WpF]UYV"OuWҍ8P'gb1|CZ$/1^~p>>fg)^ ,I nrN-Lݪ%2EK{Fq+X|VDd |h   s *A ? ?3"`? 2`M~)?2'?`!`M~)?2'` 0xSOA~3Vִ"Qj&ITDo 6-ak*7?=xh╻zIbn P {{o)$Kc7{C85h *d,Oħf-ڑ-lAa[<?f0EL}!P[KD/cT<`xd}l9T(nњ$w +]z.e˸ZUYirŬ1V# o6g䧉"*5}i)]*L-.VQc䵹Ǎ"Z/:1.D7 z=rAڃA9.` fih*lQ` ޴-؇ 9z0 (gUxJID~Iڕt3!Ty mX|$%%mN"|=X@A6A3@X\yNw{.DnKfy1j5*JJQzq^8nv6 0(2Dd HhB   S A ?  2Դگ5fB`!Դگ5f@@X-|xK@ibuVt_VQ?`b&IݿA 8.ip{} tO(t>aŨ/QB'ONQPW6 ^ЭinCzZYa@fެ(g]bR6;Z j4Mz&L;؈Ǎs5T 6e~a=!!R^ +3uKi]w__Y{\'p2PsqYp~'?I٫mc`ӫLsnȗA _:;5v4xwUۻ*D8U@(Œn W_=BU+Dd @B  S A?  2[ a-2P7gE`!/ a-2P`M(Pxcdd``~$d@9`,&FF(`T̐ & Ô %d3H1icY$\ĒʂT @_L TȠ1[IIaby`bGE@{# &brz8?X> A]˜ҡi kqEp,_wcGksB&, R!P`ZE&0xX]?a\ʉ, ;&iFPX8:a]& Ma`@7!g؅ #l`a/oqsU dE70=bBVq'.hZpp2@" F&&\raִ ] h=TDd B ' S A'? 2"n XH!`!"n  `x=KPsnb۴`P͂uvIѴ? [ Qpݡ  :~$.=Pơ[gRE$VMsӜ%=$Uy`cHT\Ju%GG楿zJXh7N,!/l*c1E=gtJ =pzx]¬5p(L.S*wd^bȧ -o1<6q}ݭE/ 8iQutojlx_=ZO |Z6ٗ!=}}rWY\wc'-Gߨnfo9'kqs'SsIoeDd  b ( c $A(? ?3"`?2 ԏ Y͏؞HJ!`! ԏ Y͏؞Hx P.8xVMLQ委DZ(#$-(Ƭ[#j@KhaALińzđY`̮a@[ط )!e;emͳ_rgS4 takr<-M|zMdjjj+{7W6>9iM[y7E[L(mdξ{0sEGbuNӔ0wةivZb8 &; AQQwDH## Ծב½NH't_OǡJMWc9әܷZ{Xe{\(joqՉ mQbm,̊d,ˬD`m&c@` -CCآ&Re9h Ѭ"˅=0"+n' Vn`⟏i|](3ejZ:Qho}S]_*Fؽ:/i#Dd ,hh  s *A? ?3"`?2K 74 UHVO`!K 74 UH2!@4|xcdd``db``baV d,FYzP1n:&B@?b (20| UXRY7S?&,e`abM-VK-WMcرsA V0ZfT T0˲YzP1}I*M*n5 , ,byف,C# #VlYH{@.\ #>8@GpV<n9fp{1L#3aj 8T?rCpl~/ʌ^Kx1@penR~;'BDW T_Zu#g Ȉϕ\Pp} v6/ `p121)W2ePdhB 0@bd`iK Dd pB  S A? 2tF/k0WP6T`!HF/k0W,`)`#@xKhAǿݤQS0mє ZQ{X[_ hE< Exѓ{U@T3Lf,;Lfv @`z4>GD8j#Ug1ë9[tAl) hǮB@z/{! &,o'Ls5迿7:mxt{|}>^gg~A{=OlZ~/ Oُq䛮efr9-_bN.]X=櫓@ w6 JfBGyήY4d9kd[ mۘpNcZb$! (9,8q\DZRo3n v'7BG1as'r૥Q;x{x %x%'KMDE;NV*f,:G) rOp8fsdv3&Gۅ}@+IeGePMA'fjް'\} fX73\Զ =Kw։-ŞUpc6$|eeVgȊAb1 bLl3p<@۵T&8/ M/hpKEjT`v>pT)x)zVbMX@tT=1\ NiŎ:*P뼤7QtzNCdža omG2ŵm!!)V,Ru?q]BckSo68Yu/xM,:V}$cn`rҲmqq5E;cg# 3# n(U#5]b7T(jiؠyz@sQCHv- 5Dd @B  S A? 2=CxSm&HN\`!CxSm&H"4hxcdd`` @c112BYL%bL0Yn&%! KA?H́깡jx|K2B* R  XB2sSRsֵ-k P.P56ZhrKd'?K2L4010' 2Ə  |)0_ηDu T7hf&3?pphABM?6j`<002q# |_59W`GaGg`dFUoQ%50@penR~0g/ )5FN 1SE [xiI[|a_OEUb8ߏO8PKɂj D }М 0F&&\vִ ] h=NDd B  S A? 2Q&yAmD3Uf!_`!Q&yAmD3Uf* e%hxKAZnR$A L)fPEO $BoE.!! nAۼIC ~c7@ ?-?u%J#jYb$k mh$̤)O0w(@ dխ\yœSd Zn+]3._jډTf@B&W#qtPd 0tA.&}9.ƃ<#xRA|.# ^mޯ锛Q0%s_Z@V~&|cQM f6g_W7~dx ~-[7J~װ"v҉lR =*M/wWSa.Dd |b  c $A? ?3"`?2xc245;脤JrTa!`!Lc245;脤Jrآ(`]?0xTKkSA>3DFJiknJ@ ަT(%75p0HT*%*uOf<]0Y!e~t!dPṈK&B'/69~?XrldJ;n[ NǕ_\ j{Pۋߌ 9|q;nGw+{`ް%6 Ev7/S=8_DL3uhk{ (㟘 w=cRCO! FD="qr8ZĠinw;$ERS9/Gԡq;*~;*2u%GA=QvKGG* ԣP7{<Óx#+["`AN=;l6 28 U#Ozq#dCZ$̈Oƃ{jXV`7oQe73s GnEcgs >΁s9p-&K]rn0xTkAMN{i{ TSjҦ_T$ևH0Rk`ARRBwJ} }?@8s46~;3w G'g$xZ%/8y^pd {ѵGM  `} 8'F!6I)G'/Ǧ ٢ɔWnjʭLJMÝU2cuŕ2=K|g}s^Ȭwpu{}C(z KLPfP&^;'] a _M=[Αq\m\%D BBtghΊȊ!"ir8bXn-.Z,(/Tq;*q;*p(hrK^<j9dz  xjK1#^ Iq8A}Nz|Z0iNibZēZ:]Vn^03H(:v2_Z dܗ1he {T~?KtQ>@Uh.MU-1֞o9F8*^` %HUulNW4anHp!(^BCHt<R##c`np=p^5_ĽgdwWɎvy'J`x4WdQP7Ŝh> `x,UGDv.3wܲرƮx̸JbHثTZckT3u>aث،Q06waќTt+ 3 ?Hn9gǔ_\ӘpeS773TzM{E#^gbZ)2u}닥B?tt+_~Ƨŧj=qjGj+Yz< =RPGj='k{k+&=ne .3ûZ`PҗΝ0;n &=J?.@P1 ȗMeXyҤH#mp `8.IEҚF\ 6WMqhliD(5Ԅ!4VFHr1וiQM?qbcf@J.(aHV !Vy-&Yh'{nM$̒OpW:>SSI#Dd TB  S A? 20zVWYmbew`!Z0zVWYmn "`04P(xcdd``6g 2 ĜL0##0KQ*faJ`QP1@@7$# PD22BaR`Z b YA01&^4AtO` ZZǰmٸ00pAaW 9TCd B_üK 4\e`jhdS3K l)Kl M7Մ4AΏ ?| "qcc0%(N?7l`;`7Ә'!NsZpD YvefCa˅쯇!|,) +ss)RH)/r s7pm!,M׆LJ yGQG ռd2 g v0o8321)W2dKsegbDa ޣEDd 0b  c $A? ?3"`?2l]8X7u81<kz!`!cl]8X7u81< kd1xSoA~3$ Rc$.M%m҃'l0DHFtZ7ʭ / y`bx0ƣ]j}o77 Z RQ[. r2ц8%KH3r1[{Xt4G:7E3 $o |TLF0aIQѪbleq ӟS洴g}^e[߆!8o񀗈r[%9T%NSsCNI";yB9aq Ս4!N+,}^ԞՆ݆fquk5۶4 ]]GlSjT~utRT\3K g7QvVݪ/[a_:Qclǁe5nLX/|[FB. C0GAkɱ$ac(X ܙxPP* `#)T_kT^OXi\1KOB$>3}GoDd B  S A? 21+3 eJ$# }`!+3 eJ$# P&(+xK$AkD`Dq\DnVu}F*ljbj`.m❉H{0p~]]= K&^t9Bƴ0 Ciuf=`6 tK)hd >VY<!Fx09s@R>R% za{"Gs\1YÍ}\dT; :M4d)7RL =H쓢'E/Bg_sڢ^ T̰;@9~3Ռ jWy]6Vb{jyRЗEna,R- e+ICDI3a+3;Q-T'qN$zt*T̎|kBauC䨸3H3!Co]|;C&ŧs_cSrׯTe׳,*SϪsty[{+7]_7  \+C![l踣% Itc17ڭu M$g˸ ȼ1Dd <TB  S A? 2^Y /Ï*"`wă`!o^Y /Ï*"`4`  XJ=xcdd``bd``baV d,FYzP1C&,7\S A?d-bc@P5< %! `Wfjv  ,L ! ~ Ay ߖ_H_5Nh8W+6VJ?D$w1䍌!+'\;0ZC0P 27)?IKf"k 2{[c߄/6悆*8·;WLLJ% iin ] @4'f~]Dd W lB  S A? 2x{(p7$R`!x{(p7$Rxm=KAggKa,D,̑;-L4B FR@l,,,DRh+Vba+V0ݞЈ-_8Rϥ;{^e0ӖޟU_U n[P\U+NkÅ!oQK9N>׃\2s bU[ !I1\t*Jiۃ3feukC2NkDd  lB  S A? 2-t"r6e8i`!-t"r6e8ixR;KA5KP "v\N,5p> /HF"B ba-ڤOڈ =X7}>0|BH:#P1mˈ8< tƻ ]݌Rj"\ll4dw|=Cda GC =yc"z~l+_<|^) 5 RZ;QK'Yb~Γ.o3aQjVx|A|6ݣB[ᬺg[mC:w F@q1'd'4¢OgF^=f{uT^bޛ(k^^z}#xGb<F<8 քs7-¿g" tͻ$$If!vh5`5 54#v`#v #v4:V l t0,5`5 544a$$If!vh5`5 54#v`#v #v4:V l t0,5`5 544a$$If!vh5`5 54#v`#v #v4:V l t0,5`5 544a$$If!vh5`5 54#v`#v #v4:V l t0,5`5 544a$$If!vh5`5 54#v`#v #v4:V l t0,5`5 544a$$If!vh5`5 54#v`#v #v4:V l t0,5`5 54/ 4a$$If!vh5`5 54#v`#v #v4:V l t0,5`5 54/ 4a$$If!vh55`555#v#v`#v#v:V P4,55`55/  / 44 Pf4T$$If!vh55`555#v#v`#v#v:V P455`55/ / 44 Pf4T$$If!vh55`555#v#v`#v#v:V P4,55`55/ / / 44 Pf4T$$If!vh55`555#v#v`#v#v:V P4,55`5544 Pf4TDd B  S A? 2}t4Tߡ`k Yq`!Qt4Tߡ`k X`Ho*x=hA߼f3zx @L6wr&eH,l^"^`.`!;+!6gcBP,R B:!R\ٙb]v޾f4S@c%0MSfD%͡[ny7ʺ BR=*4YL ;w1!'j]*. .GIVYY=F[an7ZqR[va[WlAz y(yvPGhޓoC*Bax$LJ2e,?(sF!TVs}8=o2]a2 A^ϳ3x}x$f?.c7~ ;.qգ"Uou u=!冧yӜ(^n<ȇ|J?{k^[|Ewy"Wl=.ɔ׳{p:Gz ;yN.'蹇3,ϯ{qָۂK_c[c?4 Dd B  S A? 2vs!9F_Շ;R`!Js!9F_Շ;J`8i1Pxcdd``Ve 2 ĜL0##0KQ*faJ`y /d3H1icYKxI9 "hRFN={`a (_#wxA|mpvg U &~.h^Gp1@*`F&&\ v.F@4`;vyDd b  c $A? ?3"`?&2ELQ,#; QBVF ᬍ9lEim5Q@L =q nmS13銹'юaxnoD]ԷrnE+4KDd  b  c $A? ?3"`?'2P\9:JR'x,z ,!`!$\9:JR'x,z `` (+xT_hRQιWs*YD#u?N0`!P|FAZO=cЃϽmz0CAdXs=ߟ #R J`ÒB1![I mK1inX]8{MLm ڤmj?Bȋs:'JDо$ 5a\!1?W6سv~Ru|iɛ)vX.TJ2]zi)M|^z1xGp;YUZ]XGdPζD>>"l{jyY #ȞHuRH63|t#[Ch$:ndN8{{;NPofCu?t#hLJS^HKJW*sD77?\b#yxٔ#3lObC1lsJNٮkW}WSg AH)Z-kB(ڹr!D6AvT:#X,&b!Qjg*lOͧ%*7L|j*% F6>4g=qj&GkY`^OƀpTt@s T6HA)8#N.4(Vud);1A%2y΂Q8o'c;Y!!r+J-|e-˚NG ñk˕r߳,B{K{LK2thx!j ]OcߜOAG/e!8Dd ,b  c $A? ?3"`?27M}ҴcbP^`!V7M}ҴcbP^ )@ @PV$xW_h[U=^inM' Y&iK#dmfN4# ^JTb!iK 00D2؋lчAIaÐ>ك}EW|~|&$^cń]d>$8 + WhսG`{x}١a9i4P.I[Dy&g攜/e3xyG~?xk"bazB?T`S4wRޑ}D SClG'FBQ؆sWWѾ4\O[d1y&~<5hCАA' fq/s&N71 G `4DPfkRWEv%mj싎K|-=&{H0#|³dWK+ߪ&V*O 0jGBeeWJ%on%XW+T2~A2~q WE&eR+FmU޴)mݠ%0ȍ᧠beR=CeyXriXVFժ)yFu}be.0;Ho5\שTZ6@Iս쫦rTkr3#f>5 l\jVq}8K67AJ^6y;? =iω%??Ie?,jKwxIEqC*ygc3=_\%O2S@ט9?Q槕cޗ秃 1屉 Lnfzt %9E[>-K3RjZ7RZurkKxy$<JlLiGiم.tt&҉ ś)ǰ81!q&rxMӺK7b6ֳՙ4;팛An\Ww!@֣ha{5HNQE1@S{ ·HiC6,&1b-Aakmܞmqt1B4%U51ĵhtl|1 yU!|tk7iU&T9(1%q8l/ mBH! ЌX\|M}: kS'JC80[v|UWUO$,lNEn/O,-Pr4^q t링|87 ^AkKE_]OP|N3G'Vr\4p^ ^mo^jR^Dd W lB  S A? )27#fLwY *[ɧ!`!7#fLwY *[xm;KAggch bR1o;-L>@"D# i$h+(H ?YV Ɲ…fg @e!cp8J+<_ nȏ3DDž54 ) ,aً݈ri°RTVEh@Ot#hĜgn Dº*#Xŭz[8f܀WaY"r2:;[es9Y,U\'=|eǐ7<>18gT>?Hag/IN$Nɔ.>ޫtҧln~_d~V'ZOEo*tG.z(Ţ<҉}n֘7`#,$7nS3758`TVֆe*jݻ$$IfJ!vh5`5 54#v`#v #v4:V l t0,5`5 544aJ$$IfJ!vh5`5 54#v`#v #v4:V l t0,5`5 544aJ$$IfJ!vh5`5 54#v`#v #v4:V l t0,5`5 544aJ$$IfJ!vh5`5 54#v`#v #v4:V l t0,5`5 54/ 4aJ$$IfJ!vh5`5 54#v`#v #v4:V l t0,5`5 54/ 4aJ Dd T|B  S A? *2uz ~`Q*!`!Iz ~` `XJ0xcdd`` @c112BYL%bL0Yn&&! KA?Hā깡jx|K2B* Rͤ XB2sSRsֵ-NHq}aܨg`2+!7C2 +ssX|͆#g,`4aQ\ `gC"#RpeqIj.CyKZ;C#| c>{HX$$IfJ!vh5P5 5 #vP#v #v :V l t0,5P5 5 / 4aJ$$IfJ!vh5P5 5 #vP#v #v :V l t0,5P5 5 / 4aJ$$IfJ!vh5P5 5 #vP#v #v :V l t0,5P5 5 4aJ$$IfJ!vh5P5 5 #vP#v #v :V l t0,5P5 5 4aJ\Dd |B  S A? +2;@*FbE!`!;@*Fb `8>0hxRK@}wIR0(DXpqItZ!cBEAOp*&$g{/y߽18iǒ4M dm]Q͖0TA[0!n`;m'!С,>R2R09^0{Q7[|f2 `J]Um6 'oohH2ӯbǏ}YVG,'Nέ!Q,bh)E-(HQ2fpy@|N%( k%Vo٣*akGCj -5,2{ Vcs ^]4(H iDd h * s *A*? ?3"`?,2Rtr-a.!`!&tr-a. !R4`\xVkcU?$ӾMLg棯c@3iA2Spu iȫĂ TA]ԅ. t!GpNf`EgQrrs?A"G)Ah~t)XdIvmIqq J.$F40(W{ksjv H_߈9_sh*'䚬*! uuwuS, r4Ҟ⫁s-#@ʼn$lw 3rŨG^)V#kNllc ۲o^1џȭ#`(Ct0$1'H׿ѺLE3`Sh͒d6\2\J$uR?_{$8_T.wŎ $vh8M?T7*~v.Մx .eo{j) rU/*{y]es$ר? ^TwT.oƲoXڸ|w&k?ugI6޽X4'y^('W'ϞՋs0.-o*] Z8Q|[_j̽aU"R٨J)N~Az>#r%}hK75äQ!=:gv߮FF}HZh 9)D 鍓 ije[ϵ/ 39D. WZO*-OC e8ȊI?c Q Mn( ԾVEI7,L"Ȏ`#&gٗ9YX- /@M`S{ `3^S4‚#Dd B 0 S A0? 52oo NANi`!aoo NANʎ $`8P/xcdd``vg 2 ĜL0##0KQ*faJ`QP1@@7$# PD22BaR`Z b YA01&^X,AtO` ZZǰm,\0ƒE$b`hjY2L"VaΒf,Db9Lk[Q54_#C !?Z׀T}"nc Fus'_@u38+1#72N`C6) |<$ӯ1?͆2 _/CXR W&00S@;Rg~!pх,o MbkDA-pT; 6<~P?jWl5 ͯ\< nH0y{#RpeqIj.CysWv.FPxh=$|Dd b 1 c $A1? ?3"`?62xiw|F+l `!xiw|F+l@ PVdxTKOQ>Դ#12ň $EMc2S`;CK?VFMl0҅qiH7P33Paas^s{9 R,IaJ!,{;KzMq|r .~ enJY7MXwFx/e,>Ṯ߹mN:=a!:8JzUk(E!N"c_#\'ߑDd 0lb 2 c $A2? ?3"`?72[e+uM]7`!/e+uM]kxRMo@]'i9!CJ%c\'|:eR,%Nܪ^@R8qqF\@" Wƞݙ7FD9:#Ԭ^qT5^Au.g.(w0cOTۯni7vIaԺ8cm(8M͇aw %QyvwGA՜.+,D՜.+,, hp|  %I  TitleH 6> MTWinEqns D@D NormalCJOJQJ_HmH sH tH DA@D Default Paragraph FontVi@V  Table Normal :V 44 la (k(No List 8+8  Endnote TextCJ4 @4 Footer  !@>@@ Title$01$`0a$5CJPC@"P Body Text Indent 881$^8\R@2\ Body Text Indent 2 881$^8`VT@BV Block Text( TL81$]L^8`bS@Rb Body Text Indent 3# 8T81$^8`4@b4 wrHeader  !.)@q. h8b Page NumberuIuI'()>?@ ;Us [ C j ! F  < T U ! F H , %3 $QiUVYquv%&um5 234`|}~7n#FGH*+,2 R S e !!#!-!D!E!h!u!v!!!!!!!"%"&"R"a"b"""""#%#&####$$$ $$$$"$)$*$,$5$=$>$@$J$Q$R$X$b$i$j$$$<%%%%&&&''(C(_(w(/)F):*t*****+N+++},,,-,-f-~---..+.2.3.5.G.N.O.Q.s.y.z.|............./// ///////////000000%0,0-0.0/00090@0A0k0000 101H1\1t111122J22.3K33333333334444$4%4'4B4H4I4J4K4S4T4U4444 55525L5M5Y5o55555556O6667]8u88889::5;b;m;;;<<<<v>>>>>>}?BRDGvHwHxHHIII$I%I&I,I-I.I4I5I7I8I:I;I=I>I@IAICI[I\I^IlImIqIrIsIvI0h00000000000000000000000 0000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000000000000 00000000000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 000000000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00000000000000000000000000000000000000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0000000000000000000000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00000000000000000000000000000000000000000000000@0I00@0I00@0I00@0I00I00 X @0@0I0 0  @0@0I00 I000|X  ')8:<?$*~v Z&u'*+, .\/02'346:<W?ACFHHzJMOfQ2T)-./1234679:<>?@BCDFHNUWXZ[\djkqvFq&*,>0366^77J88&:;";=;Q;i;>DCuHHHI+IUI{I`JJK:KJM4P]PPPPjQQQ"$T*,058;=AEGIJKLMOPQRSTVY]^_`abcefghilmnoprstR+s + ? A R f h g { } < P R !#*>@auwQegYmo/CEu m13  H\^`xz35G[]&(e }  ####'''_(s(u(>*V*X****,---(-*-f-z-|----////01D1F1\1p1r1111122/3G3I33334 5 5566]8q8s8888:::;;;uI::::::::::::::::::::1::::::::::::::::11::::::::11::::::::::::+25?!l,2$wAG BD@0(  B S  ?uIU*U,(ULU|U\U,***:::vI***:;;vI=*urn:schemas-microsoft-com:office:smarttags PlaceName=*urn:schemas-microsoft-com:office:smarttags PlaceType9*urn:schemas-microsoft-com:office:smarttagsplace B        B C H I N O X Y   A C ! # <>HJ  /FGIJQu4589F`{~7:;@EG   ')2 4 e G!H!L!M!Q!S!W!X!\!^!a!c!k!l!q!s!"""""#####'(((( (F)G)>*Y*Z*[*\*i*},,,,,,,,,,,,/ /11111222/3J3K3O3P3Q3]8t8u8x8y88::::::;;;;;;5I5I7I7I8I8I:I;I=I>I@IAI`IkIqIrIsIvI    ? A X Y ! # %* 38  $/Fu4`{7;n2 4 R S X [ e ! !!!#!""""###%#'(F)G)>*Y*+6+7+N+},,,,,/ /$/%/'/00 11112/3J3]8t8::5;L;N;b;m;;;;}?~??IAAAABBB&I)I*I,I.I1I2I4I5I5I7I7I8I8I:I;I=I>I@IAI`IkIqIrIsIvI333333333333333333333333333333333333333333 + F G /Fu4`{3=E F e &#&#%%&&&&&&&&'(F)G)9*9*:*:*>*Y*++++......../ /#/$/&/'/111222.3J366]8t899::;;>>4I5I5I7I7I8I8I:I;I=I>I@I`IlIlImIqIrIvI /"/5I5I7I7I8I8I:I;I=I>I@IAIqIrIvI[a$ :nQt;+`8z0~I\!|'~B=%w_6>Lib\EO4.dcmDQj@`&a Xg~)jo4.dQo']xJVir} 88^8`o(.88^8`o(.^`o(.^`o(.^`o(. TT^T`hH. $ L$ ^$ `LhH.   ^ `hH. ^`hH. L^`LhH. dd^d`hH. 44^4`hH. L^`LhH.^`o(.0^`0o(.^`o(. ^`hH. pLp^p`LhH. @ @ ^@ `hH. ^`hH. L^`LhH. ^`hH. ^`hH. PLP^P`LhH.\^`\o(.0^`0o(.hh^h`o(.808^8`0o(.^`o(. hh^h`o(. 0^`0o(.88^8`o(.88^8`o(.^`o(.z0o]x&air}\EOw_6>a$ Xg+cmDQQo[nQ\!jB=%A        ,        nmTM+YP$0  .t,BD0?qD!^$&:"(V(\(C~3JN5 W5kX6`6S:)AYD.DC2DHHzJL~?MLN %Yg'Yy[!bh8bsd{jIkGpAsL+YIDum^Ix=MnwrsHs8Np@JhRO$#EQzMsA[`S3\M& `u&8J&rD"_/@3 $ :nRz]Zs{w91}_nP*t!#!-!D!E!h!u!v!!!!!!!"%"&"R"a"b"&####$$$ $$$$"$)$*$,$5$=$>$@$J$Q$R$X$b$i$j$--..+.2.3.5.G.N.O.Q.s.y.z.|............./////////////000000%0,0-0.0/00090@0A03333333334444$4%4'4B4H4I4J4K4S4T4U4444 55525L5M5Y5o5555555vI33@Microsoft Office Document Image WriterNe01:winspoolMicrosoft Office Document Image Writer DriverMicrosoft Office Document Imag/d,,LetterwidmMicrosoft Office Document Imag/d,,Letterwidm / /cH / /  !"#$%+,-/015}?}@ABEuIP@PPPPPPPPP P"PH@P.P0Pd@P4P6P8Pt@P<P|@PDPFP@PJPLP@P@PP@PP@PUnknownGz Times New Roman5Symbol3& z Arial;WingdingsY New YorkTimes New Roman3Times  &y#f H>% H>%!;dIIj2Q;HX?2cop433T               FMicrosoft Office Word Document MSWordDocWord.Document.89q