MFE 230G (2008) Homework 4 page 3

8/29/2008

MFE 230G: Homework 4

Due: September 12, 2008

1.  You are modeling alphas as a combination of subsequent active returns (d), and random noise (Z):

1)

The independent random variable, Z, has mean 0 and standard deviation 1. Knowing that your IC=0.05, and that the active risk is 25%, what are c1 and c2? What two conditions do you need to invoke to derive them?

2.  You have tested two new investment ideas, and found the following results using the factor portfolio approach to information analysis. The first signal (below) has an overall IR of 1.32, with annual turnover of 409%. The second signal has IR=0.90, with annual turnover of 555%. Based only on this analysis, how (if at all) would you propose using these signals?


3.  In Homework 2, you used Aegis to build a long-only 2% active risk portfolio using an APT model for the alphas. Estimate the transfer coefficient for that portfolio. (Compare the forecast alpha and active risk of your portfolio to another portfolio built with short positions allowed.) Why might your transfer coefficient in a live implementation of this strategy be smaller than this estimate?

4. 
Problem 14A.2 (p. 416)

5.  You are managing a very successful mutual fund, and want to make sure you have chosen the right level of turnover. In the absence of costs and constraints, you have an information ratio of 1.2. You run the fund with an active risk of 5%. Based on your empirical experience, your fund has a transfer coefficient which looks like:

with: emax=50%

t*=60%

g=0.5

and where t measures the fund’s turnover. So the maximum efficiency is 50% (less than 100% due to the long-only and other constraints). And at 60% annual turnover, the efficiency is 32%.

You also know that your expected costs per trade have the form:

with:

and A measures the fund’s assets in $billions. So with $10 billion in assets and 60% annual turnover, the expected costs per trade are 0.64%. The annual costs at the fund level in that case would be the 0.64% times the annual turnover, or about 0.38%.

Based on these models, for asset levels between $1 billion and $100 billion, estimate the turnover level that maximizes the alpha net of costs. Please provide your answer in the form of an excel chart of turnover versus assets.

6.  Problem 17.1, p. 508-509.

7.  Problem 17.2, p. 509.

8.  Problem 17.4, p. 509.