Question

Given a simple world with two assets, a bond fund and a stock fund, clearly detail the steps involved in arriving at the 1) efficient frontier, and 2) market (optimal) portfolio.

Answer 1

The efficient frontier shows the lowest level of standard deviation for a given level of return or highest return for a given level of standard deviation.

The efficient frontier graphically represents portfolios that maximise returns for the risk assumed. Returns are dependent on the investment combinations that make up the portfolio.

Steps on arriving at the efficient frontier:

Suppose The expected returns, the standard deviations and the correlation of the two assets are as per the below table. We have to obtain the portfolio expected return and portfolio standard deviation associated with each weight of the assets as shown below:

E(A) =	12.00%	SD(A)=	18.00%
E(B)=	9.00%	SD(B)=	10.00%
rho(A, B)=	-0.15
		Portfolio SD	Portfolio expected return
w1	0.1	8.91%	9.30%
	0.2	8.27%	9.60%
	0.3	8.17%	9.90%
	0.4	8.65%	10.20%
	0.5	9.62%	10.50%
	0.6	10.94%	10.80%
	0.7	12.51%	11.10%
	0.8	14.24%	11.40%
	0.9	16.08%	11.70%
	1	18.00%	12.00%

Nest we plot the portfolio frontier from the data of the above table as shown below:

Here we see that the portfolio frontier can be divided into two parts.

The upward sloping curve and the downward sloping curve

Points on the downward sloping curve have lower returns but higer risk.

So according to the mean variance framework an investor will choose a portfolio on the upward sloping curve since it maximises his returns

Steps on arriving at the optimal portfolio:

The steps are shown in the below image: