1. The $250M Arroyo Fund has completed its ten-year life. Its annual performance details are described Q1 below

	Expected Return
Company A	10%
Company B	15%
Covariance matrix
	A	B
A	0.0144	0.0066
B	0.0066	0.0484

a. Compute the value multiple, realized value multiple, unrealized value multiple, and IRR for Arroyo after every year of its life.

b. At the end of Arroyo Funds life, what is its final GVM and GP%? Show your calculations.

2. Aggie Partners is raising their first fund, Aggie Partners Fund I, with $200M in committed capital, annual management fees of 1.75 percent, carried interest of 20 percent, and a carried interest basis of committed capital. The three individuals on the Aggie team have previously managed the captive VC portfolio for the Presidio family. During the 10 years of managing the Presidios VC portfolio, the partners did not charge management fees or carried interest, and they achieved an unknown GVM equal to K.

a. For any given K, solve for the carried interest, value multiple, and GP%.

b. How large must K be for the value multiple to be greater than 3?

c. How would your answer to parts (a) and (b) change if the carry basis were equal to investment capital?

3. The Largeco pension fund aggregates its entire portfolio every month across all asset classes and computes its net returns, Ri. Q3 tab of hw2.xls displays these monthly returns for one year, along with the market returns and the risk-free treasury bill rates for those months. Use Equations (4.1) and (4.2) in Chatper 4 of the VC book to estimate the beta, alpha, and cost of capital for the Largeco portfolio. You can use 2.5% for risk-free rate and 6% for market premium. (In Excel, =slope(known_ys, known_xs) and =intercept(known_ys, known_xs) can be used to estimate the slope and the intercept (constant term) of a linear regression.)

4. Suppose you are forming a portfolio with Company A and Company B, which have expected returns and covariance matrix as in Q4 tab of hw2.xls.

a. Construct portfolios consisting of the two stocks with a wide range of portfolio weights (e.g., 10%:90%, 20%:80%, etc.) Plot the portfolios on a chart with expected return on the y-axis and volatility on the x-axis.

b. What are the portfolio weights of your minimum-variance portfolio?

c. What range of portfolio weights produce inefficient portfolios?

d. Now, suppose you can save/borrow at the risk-free rate of 3%. What is the expected return and volatility of the tangent portfolio, and what are its portfolio weights?

5. Talltree Ventures has raised their $250M fund, Talltree Ventures IV, with terms as given in Appendix 2.B of the VC book (see Chapter 2). Construct an example of fund performance where the clawback provision would be triggered. In this example, compute the carried interest paid in each year, and show the total amount that must be paid back by the GPs upon the liquidation of the fund.