Question

Consider an investor with a 3 asset portfolio. Fifty percent of the investor’s portfolio is invested in common stock with an expected return of 11%, an additional thirty percent of the investor’s portfolio is invested in corporate bonds with an expected return of 6%, while the remaining twenty percent of the portfolio in invested in real estate which offers an expected return of 14%. The standard deviation of return for the three individual investments are 23%, 9%, and 32% respectively. If the correlation coefficient between the stock and bond returns is 0.60, the correlation coefficient between the bond and real estate returns is 0.70, and the correlation coefficient between the stock and real estate returns is 0.80, what is the standard deviation of expected return for this portfolio?

PLEASE EXPLAIN ALL STEPS!!

Answer 1

	Proportion	Expected return	Standard Deviation
Common stock	50%	11%	23%
Corporate bonds	30%	6%	9%
Expected return	20%	14%	32%

Combination	Correlation coefficient
Common stock and corporate bonds	0.60
Corporate bond and real estate	0.70
Common stock and real estate	0.80

Expected return computation

	Proportion	Expected return	Proportion weighted return
Common stock	50%	11%	5.50%
Corporate bonds	30%	6%	1.80%
Expected return	20%	14%	2.80%
Expected return of portfolio ---> Total of Proportion weighted return	10.10%

Standard Deviation computation

	Proportion	Standard Deviation	Proportion x Standard Deviation	Square of Proportion x Standard Deviation
Common stock	50%	23%	11.50%	1.32%
Corporate bonds	30%	9%	2.70%	0.07%
Expected return	20%	32%	6.40%	0.41%
Step 1 : Sum of (Square of Proportion x Standard Deviation)	1.81%
Step 2 : 2 x Proportion of stock x Standard Deviation Of stock x Proportion of Bond x Standard Deviation Of Bond x Correlation Coefficient of stock and bond	0.37%
Step 3 : 2 x Proportion of bond x Standard Deviation Of bond x Proportion of real estate x Standard Deviation Of real estate x Correlation Coefficient of bond and real estate	0.24%
Step 4 : 2 x Proportion of stock x Standard Deviation Of stock x Proportion of real estate x Standard Deviation Of real estate x Correlation Coefficient of stock and real estate	1.18%
Step 5 : Step 1+Step 2+Step 3+Step4	3.60%
Step 6 : Square root of Step 5 ---> Standard Deviation of portfolio	18.97%

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