Question

please work all parts.

2. Stock A has expected return of 14% and volatility 30%. Stock B has expected return of 8% and volatility 19%. The correlation between two stocks is -0.2. The risk free interest rate is 4% (a) Find the expected returns, volatilities, and Sharpe ratios of portfolios that maintain 100.0% investment in Stock A and 100(1-x)% in Stock B, where x is given in the following table. Volatility Expected return Sharpe ratio 0.8 0.9 1.0 (b) How to create the tangent portfolio. Compute its expected return, volatility, and Sharpe ratio. (c) Construct an efficient portfolio that has a total of investment of $10,000 and expected return of 10%. What is the volatility of this portfolio? (d) Construct an efficient portfolio that has a total of investment of $10,000 and volatility of 20%. What is its expected return?

Answer 1

(a).

	Volatility	Expected return
Stock A	0.3	0.14
Stock B	0.19	0.08
Risk free interest rate%	4
R(f)
Correlation Co-efficient	-0.2
Stock A	Stock B	Volatility%	Expected return%	R(p)-R(f)	Sharpe Ratio
x	(1-x)	(σ)	R(p)		{R(p)-R(f)/σ}
1	0	30.00	14.00	10.00	0.33
0.1	0.9	16.76	8.60	4.60	0.27
0.2	0.8	15.18	9.20	5.20	0.34
0.3	0.7	14.49	9.80	5.80	0.40
0.4	0.6	14.81	10.40	6.40	0.43
0.5	0.5	16.07	11.00	7.00	0.44
0.6	0.4	18.08	11.60	7.60	0.42
0.7	0.3	20.63	12.20	8.20	0.40
0.8	0.2	23.54	12.80	8.80	0.37
0.9	0.1	26.69	13.40	9.40	0.35
1	0	30.00	14.00	10.00	0.33

(b). The tangent portfolio is the portfolio having highest sharpe ratio. From the above calculation is is evident that highest sharpe ratio is 0.44 at the portfolio having weights of 50% in stock A and 50% in stock B.

For this portfolio, as calculated above:

Expected return%	11.00
Volatility%	16.07
Sharpe Ratio	0.44

(c). From above calculations in (a) it is clear that the expected return of 10% lies in between weights of stock A having 0.3 and 0.4. Therefore in proportionally weight of stock A would be 33.33% and stock B would be 66.67% to have an expected return of 10%.

Volatility of this portfolio with above percentage of weights is 14.48%

Volatility = $10,000*14.48% = $1,448

(d).From above calculations in (a) it is clear that the volatility of 20% lies in between weights of stock A having 0.6 and 0.7. Therefore in proportionally weight of stock A would be 66.67% and stock B would be 33.33% to have an expected volatility of 20%.

Expected return of this portfolio with above percentage of weights is 12.00%.

Expected Return = $10,000*12.00% = $1,200

Note:

all the above calculations are done by using the below formula:

Expected Return = {W(A)*R(A)}+{(W(B)*R(B)}

Volatility = Square root of {(W(A)^2)*(V(A)^2)}+{(W(B)^2)*(V(B)^2)}+2(W(A))(W(B))(V(A))(V(B))(Correlation Co-efficient)

Where,

W(A) = Weight of Stock A

W(B) = Weight of Stock B

R(A) = Expected Return of Stock A

R(B) = Expected Return of Stock B

V(A) = Volatility of Stock A

V(B) = Volatility of Stock B