Reference no: EM132186789

Question 1. You consider investing in two mutual funds (i.e. particular portfolios Δ1, Δ₂) with the parameters as described in Table 1, The funds are valued in a market where investors can borrow and lend, using ZCB, at a risk free rate of 5%, have common beliefs, and require an excess return of 8% for holding the market portfolio.

(a) The m^th asset has β_m = Cov(r_m, r*)/Var(r*) where r_m, r* are the (random) returns of the security and market portfolio respectively. In a similar manner, for a given portfolio Δ, we define β(Δ) ^Δ= Cov(r(Δ), r*)/Var(r*), and these are the values given in Table 1, With Δ^Tβ^→ and hence the vector of security β's, show that β(Δ) = Δ^Tβ^→ and hence the portfolio Δ satisfies the CAPM formula

r^→(A) = r_f + β(Δ)(r‾* - r_f).

(b) If, for a given target return, you are volatility averse, which of the two funds do you prefer and why?

Question 2. SocialCom has filed an initial public offering (IPO), and you are given the task to analyze the amount of capital SocialCom will be able to raise from the financial markets through this IPO. You feel the SocialCom IPO is similar to that of Linkedin from 2011.

The excel sheet "Linkedin.xlxs" provides historical data on the daily returns of Linkedin from October 10, 2011, through October 8, 2013 (Column A). The excel sheet also contains daily returns of the S&P 500 index (Column B) and the yield of the 3-month Treasury bill (a proxy for the risk free rate - Column C), Data is sorted newest to oldest.

(a) What's the daily average return for Linkedin during the sample period? What's the average daily return of the S&P 500? What's the average daily yield?

(b) Compute the empirical beta of Linkedin for two subperiods: (i) October 10, 2011, through October 8, 2012, and (ii) October 9, 2012, through October 8, 2013.

(c) What are the expected daily returns that CAPM implies for Linkedin for the subperiods (i) and OW What are the average daily returns of Linkedin during these two sub-periods? The difference (i.e, actual average less CAPM implied) between the two daily returns in commonly referred to as the "alpha" of the security. For each subperiod, compute the alpha of Linkedin.

(d) For each subperiod, compute the total volatility, systematic volatility, and the idiosyncratic volatility of Linkedin as implied by CAPM.

(e) Compare the alpha, the beta, and the idiosyncratic volatility of Linkedin over the two subperiods. What does this tell you about how the market was pricing Linkedin right after its FPO?

(f) Assume that SocialCom will perform, right after its IP°, the same way that Linkedin performed after its IP°. In other words, assume that the beta. of SocialCom is the same as the beta of Linkedin in subperiod N. The current valuation of SocialCom is $12.8 billion. What is the expected valuation of SocialCom implied by CAPM right after its IPO?

(g) The market currently estimates that SocialCom's valuation will rise to $14 billion on its first day of trading in the market. What does this tell you about the alpha that the market is anticipating for SocialCom? Is a. valuation of $14 billion justified within CAPM? If not, what reasons do you believe are leading to a deviation from CAPM?

In problem 5, use Excel to solve the problem, turn in the code (or Excel file), also written the statement, for example:

"Using the AVERAGE and CORREL commands in Excel, I find the empirical average and correlations of the data to be ...."