Question

You are a portfolio manager that is interested in incorporating a new share in your portfolio multi-asset portfolio. Your portfolio currently holds bonds therefore you are faced with a simple two-asset problem. Assuming a risk-free rate of 6% and the data in the table below:

Data	Share_A	Share_B	Share_C	Bonds
Expected Return	14%	12%	11%	9%
Standard Deviation	13%	15%	11%	3%
Covariance with Bonds	0.003	0.0016	0.0022	NA

Please calculate:

1. The optimal weight in a share versus your current bond holding

2. The return of the new portfolio (made up of one share and your bond holding)

3. The risk of the new portfolio ((made up of one share and your bond holding)

Answer 1

Expected return on the portfolio = w(x)*E(x) + w(y)*E(y)

Standard deviation of portfolio =

where x and y are the securities

We choose the weights such that the Sharpe ratio is maximised

Sharpe ratio = (Portfolio return-Riskfree rate)/Standard deviation of the portfolio

We calculate the optimal 2-asset portfolio using excel solver

Enter any random weights, let's say 0.5 and .0.5 for Share B

For Share B and Bond, enter the following constraints in excel solver (To maximise the Sharpe's ratio)

Solving we get

Similarly, the steps are repeated for other Share and bond combination

1. The optimal weight in a share versus your current bond holding

Share A and the bond gives the highest Sharpe's ratio

Hence, optimal weights:

Share A weight = 12.4%

Bond weight = 87.6%

2.The return of the new portfolio (made up of one share and your bond holding)

Return of Share A and the bond portfolio = 9.62%

3.  The risk of the new portfolio ((made up of one share and your bond holding)

The risk of Share A and the bond portfolio (standard deviation) = 3.087%