Your investment strategy is to maximize expected return but with a risk level (s
ID: 2756973 • Letter: Y
Question
Your investment strategy is to maximize expected return but with a risk level (standard deviation) that does not exceed 15%. Since you are a CAPM believer, you hold a combination of the market portfolio and risk free asset. The market expected return in 10% with a standard deviation of 20% and the risk free rate is 3%.
(A) What portfolio do you hold?
ANSWER (A)
Answer: The portfolio would consist of 75% market portfolio and 25% risky asset.
The Standard deviation of a portfolio containing a risky asset (here the market portfolio) and a risk free asset is given by the formula
Standard deviation of the Portfolio = Weight of the risky asset * Standard deviation of the risky asset.
For the porfolio to have a risk level of 15% (std deviation) the weight of the market portfolio can be solved from
the equation 15 = Wt of the risky asset * 20 ; Wt of the risky asset = 15/20 = 0.75.
Therefore the portfolio would consist of 75% market portfolio and 25% risky asset.
The expected return would be 0.75*10 + 0.25*3 = 8.25%.
Derivation of the formula for a portfolio with a risk free asset.
of the risky asset. Hence, the standard deviation of the portfolio = weight of the risky asset in the portfolio * standard deviation of the risky asset.
NASA has just announced that it not only found water on MARS but it also plans to open a resort on MARS named “MARS for Life”. NASA wishes to sell the new venture to investors in an initial public offering (IPO). An analyst estimates expected profits (Revenues – Expenses) would be $1B one year from now. The analysts mention that these are the expected profits and the risk (standard deviation) of this venture is 30% and the correlation with the market is 0.2. For simplicity we assume that this is a 1 year project where all revenues and expenses occur 1 year from now.
Q: 1 In the public offering NASA plans to sell 50M shares. What is the maximal share price at which you will invest in the new venture?
ANSWER Q:1
Standard Deviation = 30%
Correlation with Market = 0.2
Required rate of return (R) = 0.2*30% = 6%
Net Cash Flows after 1 year = $1 Billion
To calculate future value of net cash flows, we have to discount the net cash flows with R
Future Value of net cash flows = 1,000,000,000/(1.06)
= $943,396,226
Thus the future value of cash flows available to all shareholders = $943,396,226
No of shares = 50,000,000
Thus the future value of cash flows available for each share = $943,396,226/50,000,000 = $18.87
Thus, the maximum price at which i will invest in teh venture is $18.87 per share
Q: 2 Suppose that the price for “MARS for Life” is 10% lower than your answer in Q: 1. How would your answer to Part (A) change? What portfolio would you hold?
PLEASE ONLY ANSWER Q:2 . I INCLUDED THE ANSWERS OF PART A AND Q:1 GIVEN BY CHEGG EXPERTS PREVIOUSLY ON MY POSTS FOR THE REFERENCE FOR ANSWERING Q:2
Explanation / Answer
Answer -2 If Price of MARS for Life is 10 % lower, Value of per share will be
= 18.87-18.87*10%
= 16.98/ share
If value will 16.98/share total Future value will be
= 16.98*50000000
= 849000000
Required rate of return = 1000000000/849000000
= 1.177 = 1.18 = 18%
Standard deviation will be = 18/0.2 = 90%
Wt of this asset = 15/90 = 0.1666= 17 %
We hold 17% of the portfolio.
Future Value of return = 943,396,226
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.