19.6. TEST YOUR UNDERSTANDING: BASICS OF THECAPM 743
Expected Covariances
excess return HBC BTT
HBC 0.11 0.04 0.01
BTT 0.08 0.01 0.02(a) Vary the weight of HBC from 0 to 1 by increments of 0.1, and compute
how the portfolio covariance risks of HBC and BTT change as a function
of the weightsxHBCandxBTT= 1−xHBC.
(b) Find the optimal weights ofxHBCandxBTT= 1−xHBCand the average
risk aversion.
(c) If the total value of the PRL stock market portfolio is 1,000, what is the
value of HBC and BTT?- Consider the following covariance matrix and expected return vector for assets
1, 2, and 3:
V =
0 .0100 0.0020 0. 0010
0 .0020 0.0025 0. 0030
0 .0010 0.0030 0. 0100
E( ̃rj) =
0. 0330
0. 0195
0. 0250
(a) Compute the expected return on a portfolio with weights for assetsj=
0 ,...,3 equal to [0. 2 , 0. 4 , 0. 2 , 0 .2], when the T-bill (asset 0) yields a return
of 1 percent. Do so directly, and then via the excess returns.
(b) Compute the variance of the same portfolio.
(c) Compute the covariance of the return on each asset with the total port-
folio return, and verify that it is a weighted covariance.
(d) Is the above portfolio efficient?
(e) Are the following portfolios efficient?- weights (0. 7 , 0. 1 , 0. 1 , 0 .1) for assetsj= 0,..., 3
- weights (0. 6 , 0. 2 , 0. 1 , 0 .1) for assetsj= 0,..., 3
(f) What is the portfolio held by an investor with risk-aversion measure
λ= 2.5?
(g) Assume that there are no “outside” bills, that is, all risk-free lending and
borrowing is among investors. Therefore the average investor holds only
risky assets. What is the portfolio composition? What is the average
investor’s risk-aversion measureλ?