Question

n the last 20 years, the average return on stock is 9.27% and the standard deviation is 18.32%. The average return on 10-year treasury note is 5.70% and the standard deviation is 8.82%. The correlation between stock and bond return is -0.5926.

1.What is the standard deviation of a 50% stock 50% bond portfolio?

2.Based on (1), In this period, the average risk-free rate is 2.14%. What is the Sharpe ratio of the 50% stock 50% bond portfolio?

Answer 1

1.Standard Deviation of Portfolio =   (( Weight of Stock * Standard Deviation of Stock)² + ( Weight of Bond* Standard Deviation of Bond )² +2 * Weight of Stock * Weight of Bond * Standard Deviation of Stock * Standard Deviation of Bond * Correlation coefficient)^0.5 = ((50%* 18.32%)² +(50%*8.82%)² - 2*50%*50%*18.32%*8.82%*0.5926)^0.5 = 7.45%

2. Expected Return = Weight of Stock * Return of Stock + Weight of bond * Return of Bond = 50%*9.27%+50%*5.70% = 7.49%
Sharpe Ratio = ( Return of Portfolio - Risk free rate)/Standard Deviation = ( 7.49% - 2.14%)/7.49% = 0.7152 or 0.72

Please Discuss in case of Doubt

Best of Luck. God Bless
Please Rate Well