By Petr Adamek, John Y. Campbell, Andrew W. Lo, A. Craig Mackinlay, Luis M. Viceira

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**Example text**

2 except that 2 = 0:006 instead of 0:003. Using this value for 2 , we have 1 = 1:162 and 2 = 1:225 giving P1 = 21:3% and P2 = 23:3%. 4) 0 = a ; ( aop op + ap p ) since Cov Rp Rop ] = 0. The result 2 = ap is immediate, thus we need to show that 1 = 1 ; ap and 0 = 0 to complete the solution. Let r be the minimum variance portfolio with expected return equal to that of portfolio a, a = r . 5) Rr = (1 ; )Rop + Rp where = ( r ; op )=( p ; op ). 8) r = rop op + rp p : Portfolio a can be expressed as portfolio r plus an arbitrage (zero-investment) portfolio a composed of portfolio a minus portfolio r (long a and short r).

If b = 1 then we are back to the previous case. Since all agents have the same utility function and face the same probability of being in each group, they all have the same expected endowment and are identical ex-ante. However, ex-post their endowments will di er,so there will be ex-post heterogeneity. As before, consider buying of the asset. 13) p = 2 (b 2;(ba);+a)a+(1ba; b) m which gives the previous result when b = 1, and p = (1 ; a) m when b = a. 17) Since 0 < a 1, R(b) R(a). Therefore, heterogeneity in the form of individual uninsurable risk increases the expected return on the asset.

9) Ra = Ra ; Rr : Since a = r , the expected return of a is zero. 10) c 25 26 PROBLEMS IN CHAPTER 5 is c = 0. Any other solution would contradict q being minimum variance. 12) Cov Rq Ra ] = 0: Thus the return of a is uncorrelated with the return of all minimum variance portfolios. 16) we have 1 = aop = 1 ; ap . 16) gives 0 = 0 which completes the solution. 1) for N assets. m we can calculate the (N 1) vector of covariances of the N asset returns with the market portfolio return, the expected excess return of the market, and the variance of the market return, Cov Z Zm ] = !

### A Solution Manual To The Econometrics Of Financial Markets by Petr Adamek, John Y. Campbell, Andrew W. Lo, A. Craig Mackinlay, Luis M. Viceira

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