Question

9. (Market portfolio, CML) In the Golkoland stock market, there are only two listed stocks, Xirkind and Yirkind. The risk-free rate of return in Golkoland is 5%, and the portfolio of Xirkind and Yirkind stocks which has the highest Sharpe ratio is given below: A C 3 Average return 4 Variance of returns 5 Standard deviation 6 Covariance of returns 7 Correlation 8 Risk-free return B DE Xirkind Yirkind 19.84% 15.38% 0.1575 0.1378 39.68% 37.12% <-- SQRT(C4)! -0.0110 -0.0747 <-- =B6/(B5*C5) 5.00% 9 0.546 0.454 <-- =1-B11 10 Highest Sharpe ratio 11 Weight of Xirkind 12 Weight of Yirkind 13 14 Portfolio return 15 Portfolio variance 16 Portfolio standard deviation 17 Sharpe ratio 17.81% 0.0699 <-- =(B11^2) *B4+(B12/2)*C4+2 B11*B12*B6 26.43% <-- SQRT(B15) 0.485 <-- =(B14-B8)/B16 a. What is the market portfolio M in Golkoland? b. What is the equation of the capital market line (CML) in Golkoland? c. What does the CML mean, and why are we interested in it? d. What is the expected return and standard deviation of a portfolio composed of 30% of the risk-free asset and 70% of the market portfolio? e. Suppose an investor wants the same return as the above portfolio (part d) but invests only in the risk-free asset and a portfolio com posed of equal weights of Xirkind and Yirkind stocks. What will be the standard deviation of the returns of his portfolio? How do you explain the difference in standard deviations between this question and in part d?

Answer 1

a) Market Portfolio M, is the combination of Xirkind and Yirkind, which results in highest sharpe Ratio

As given, highest sharpe ratio comes out 0.485 when Xirkind weight is 54.60% and Yirkind weight is 45.40%.

There Market Portfolio M will be portfolio of xirkind and Yirkind where Xirkind weight is 54.06% and Yirkind weight is 45.40%.

b)

Equation of CML is

ERm - R ER, = Rp + SD, X- SDM

ERp= Expected Return of Portfolio

Rf= Risk-Free Rate i.e. 5%

SDp=Standard Deviation of Portfolio

ERm=Expected Return of the Market Portfolio i.e. 17.81%

SDm=Standard Deviation of Market Portfolio i.e. 26.43%

ERp = 5% + SDp X ( 17.81%-5%) / 26.43%

ERp = 5% + SDp X .485

c) CML is optimal combination of a risk-free asset and the market portfolio. Capital Market Line is a line from the risk-free rate of return which is tangential to the efficient frontier. Tangency Point Portfolio is the most efficient portfolio, which is also called as Market Portfolio. Moving up the Capital market line will increase the risk of the portfolio and moving down will decrease the risk. We are interested in CML as it tangency point gives the most efficient portfolio.

d)

	Weight	Return	Standard Deviation
Risk Free Asset	30%	5%	0%
Market Portfolio	70%	17.81%	26.43%

Expected Return = Wf x Rf + Wm X Rm

Expected Return = 5% X .30 + 17.81% X .70

Expected Return on Portfolio = 13.97%

Where,

Wf = Weight of Risk Free Asset i.e. 30%

Rf = Return of Risk Free Asset i.e. 5%

Wm = Weight of Market Portfolio i.e. 70%

Rm =Return of Market Portfolio i.e. 17.81%

Standard Deviation of Risk Free Asset is Zero (0). Therefore, Standard Deviation of Portfolio will be Market Portfolio Standard Deviation times the Weight of Market Portfolio

Standard Deviation = 26.43% X .70

= 18.50%

e)

Step 1 – Calculation of Return and Standard Deviation of Portfolio with equal weight in Xirkind and Yirkind

	Weight	Standard Deviation	Return
Weight of Xirkind	50%	39.68%	19.84%
Weight of Yirkind	50%	37.12%	15.83%
Correlation Cofficient	-.0747

Return of Portfolio with equal weight = 19.84% X .50 + 15.83% X .50

= 17.83%

Standard Deviation of Portfolio with equal weight in Xirkind and equal weight in Yirkind will be

Standard Deviation = (W1 × σ1 )2+(W2 × σ2 )2+2 ×W1 ×W2 ×σ1 ×σ2 ×corr (1,2)

(.50 × 39.68 )2+(.50 × 37.12 )2+2 ×.50 ×.50 ×39.68 ×37.12 ×-.0747

= 26.14% (rounded off)

Where,

W1= Weight in Xirkind i.e. 50%

W2= Weight in Yirkind i.e. 50%

σ1 = Standard Deviation of Xirkind i.e. 39.68%

σ2 = Standard Deviation of Yirkind i.e. 37.12%

Corr(1,2) = Correlation Coefficient between Xirkind and Yirkind

Step 2

Standard Deviation of Risk Free asset is Zero (0). Therefore, standard deviation of portfolio is 26.14% X .70 = 18.30%

The standard deviation in d part comes out to be 18.50%, the difference arise because of decrease in standard deviation of the Portfolio of Xirkind and Yirkind, since weight of Xirkind which has higher standard deviation has been decreased and weight of Yirkind has been increased, which has lower standard deviation.