Question

How does the portfolio possibility curve look like if you have a portfolio consisting of asset A (a share with a volatility of 10% and an expected return of 8%) and asset B which is risk-free (rf 1%)?

Please sketch the curve and indicate clearly the min. variance and the max. sharpe point.

Another question from me relating this question: what would the sigma (variance) of a risk-free asset be?

Answer 1

Portfolio Possibility Curve is also known as Efficient frontier curve which tells us set of optimal portfolios (share of two assets in a portfolio) that offer highest expected return over a given risk level (standard deviation/variance) or lowest risk at a specified return.

As per the figures provided in question,

Asset A: Return = 8% Risk = 10%

Asset B: Return = 1% Risk = 0% (since, it's risk free)

The portfolio possibility curve would look like as below,

Portfolio Possibility Curve (Efficient Frontier Curve) Return 0% 0% 2% 4% 8% 10% 12% 6% Risk

The curve has been made with following weights of each asset. At each point, variance of the portfolio is calculated by using below formula and expected return is calculated using weighted average method.

Weight	Weight	Standard	Expected
Security 1	Security 2	Deviation	Return
1.0	0.0	0.10000	0.08000
0.9	0.1	0.09000	0.07300
0.8	0.2	0.08200	0.06740
0.7	0.3	0.07000	0.05900
0.6	0.4	0.06000	0.05200
0.5	0.5	0.05000	0.04500
0.4	0.6	0.04000	0.03800
0.3	0.7	0.03000	0.03100
0.1	0.9	0.01236	0.01865
0.1	0.9	0.01000	0.01700
0.0	1.0	0.00000	0.01000

Oportfolio = wo + wc +2w, W221,2010 W = Where: W = Proportion of the portfolio invested in Asset 1 Proportion of the portfolio invested in Asset 2 01 = Asset 1 standard deviation of returns 0 = Asset 2 standard deviation of returns P2 = Correlation coefficient between the returns of Asset 1 and Asset 2

The Minimum Variance Portfolio is when the risk is minimum. In this case, asset A (share = 0%) and asset B (share = 100%) will be Min Variance portfolio as the risk will be 0% and the return will be 1%.

The max Sharpe ratio point will be all the points on the curve except when the return and risk both are zero. Sharpe ratio is 0.7 in each case. It is calculated by using formula (Rp-Rf)/SigmaP.

The sigma of risk free asset would be 0 because it provides constant return without any volatility.