Question

Suppose you estimated the following data for funds GMO and OMG. The correlation coefficient between them is 0.35. The risk-free rate is 5%. E(R) ? GMO 19% 29% OMG 8% 15%

a.) Mango fund invests 45% in GMO and the remaining in OMG. What are the E(R), ?, and Sharpe ratio of Mango?

b.) Among all possible portfolios formed from GMO and OMG funds, Mingo has the lowest variance. What are the E(R), ?, and Sharpe ratio of Mingo?

c.) Fund Optigo chooses to invest in GMO and OMG with the highest possible reward-tovolatility ratio. What are the E(R), ?, and Sharpe ratio of Optigo?

d.) Suppose your client Linda wants to allocate her investment between the Optigo fund and the risk-free assets. She hopes to limit her risk to 10%. How do you allocate Linda’s money to T-bills, OMG, and GMO? What is her Sharpe ratio? [Hint: Capital allocation problem.]

Answer 1

The portfolio’s expected return is a weighted average of its individual assets’ expected returns, and is calculated as:

E(Rp) = w₁E(R₁) + w₂E(R₂)

Where w₁, w₂ are the respective weights for the two assets, and E(R₁), E(R₂) are the respective expected returns.

a) E(R) mango= 19*.45+8*0.55=12.95%

Op = Vwł oʻ(ka)+ wą o²(kg)+2WA Wg R(ka,kg )o(ka)o(ks)

Ka= GMO, Kb= OMG

	GMO	OMG
er	0.19	0.8
std dev	0.29	0.15
weight	0.45	0.55
std dev square (1)	0.0841	0.0225
weight square (2)	0.2025	0.3025
(1)*(2)	0.01703	0.006806

std dev of portfolio= 8.6%

Sharpe Ratio=Rp​−Rf/std dev ​​

where:Rp​=return of portfolio

Rf​=risk-free rate

σp​=standard deviation of the portfolio’s excess return​

12.95-5/8.68= 0.9158