Question

In addition to risk-free securities, you are currently invested in the Tanglewood Fund, a broad-based fund of stocks and other securities with an expected return of 10% and a volatility of 26%. Currently, the risk-free rate of interest is 5%. Your broker suggests that you add a venture capital fund to your current portfolio. The venture capital fund has an expected return of 22%, a volatility of 82%, and a correlation of 0.2 with the Tanglewood Fund. Assume you follow your broker's advice and put 50% of you money in the venture fund:

a. What is the Sharpe ratio of the Tanglewood Fund?

b. What is the Sharpe ratio of your new portfolio?

c. What is the optimal Sharpe ratio you can obtain by investing in the venture fund? (Hint: Use Excel and round your answer to two decimal places.)

a. What is the Sharpe ratio of the Tanglewood Fund? (Round all intermediate values to five decimal places as needed.)

The Sharpe ratio of the Tanglewood Fund is _________ (Round to two decimal places.)

b. What is the Sharpe ratio of your new portfolio? (Round all intermediate values to five decimal places as needed.)

The Sharpe ratio of your new portfolio is _________ (Round to two decimal places.)

c. What is the optimal Sharpe ratio you can obtain by investing in the venture fund and what would be the percentage invested in the venture fund in the optimal portfolio? (Hint: Use Excel and round your answer to two decimal places.) (Round all intermediate values to five decimal places as needed.)

The optimal Sharpe ratio you can obtain by investing in the venture fund is ___________ and the percentage in the venture fund would be ____________(Round first answer to two decimal places and second answer to the nearest whole number.)

Answer 1

Given:

Corelation	0.2
rf	5%
	Return	Std Dev
Tanglewood Fund	10%	26%
VC fund	22%	82%

a) Sharpe ratio of Tanglewood fund where Rt is return on Tanglewood fund, rf is risk free rate, is std dev of Tanglewood fund

SR = (10%-5%) / 26% = 0.1923

b) If 50% money is put on Venture Capital Fund

wt = 50% (Weight of Tanglewood fund)

wv = 50% (Weight of VC fund)

Portfolio return = wt*Rt + wv*Rv = 0.5*10% + 0.5*22% = 16%

Portfolio Std Deviation =√(W2tσ2t + W2vσ2v + 2WtWv*Cov(t,v))

Cov(t,v) = = 0.2*0.26*0.82 = 0.04264

Portfolio Std Deviation =√(0.52 * 0.262 + 0.52 * 0.822+ 2*0.5*0.5*0.0462 = 0.454225 = 45.42%

Sharpe Ratio = (Rp-rf) / = (16%-5%) / 45.42% = 0.24217

c)

Proportion of Tanglewood fund in optimal risky portfolio
Wt=	(Rt-rf)*σ2v - (Rv-rf)Cov (t,v)
	(Rv-rf)*σ2t + (Rt-rf)σ2v -(Rt-rf+Rv-rf) (Cov (t,v)
Wt=	73.8044%
Wv= (1-Wt) = 1-0.738044 =	26.1955%
Portfolio Return E (R )=	Wt*Rt+Wv*Rv =0.738044*0.1 + 0.261955*0.22 =	13.1435%
Portfolio Std Dev σp	√(W2tσ2t + W2vσ2v + 2WtWv*Cov(t,v)) = √ (0.7380442 * 0.262 + 0.2619552 * 0.822+ 2*0.738044*0.261955*0.0462 =	31.5358%
Sharpe Ratio (Risk to Reward)	E(Rp)-rf	E(Rp) is return of optimal risky portfolio
	σp	σp is std dev of optimal risky portfolio
SR=	=(13.1425%-5%) / 31.5358% = 0.2582