Question

Part 1:

You are a wealth manager revising the portfolio allocation for your client who currently holds a portfolio of stocks and bonds (the “SB fund”) that has performed well. You are considering adding gold to this fund. Based on your research, you forecast the following distributional properties of the annual returns on the SB fund and gold:

Asset	Expected return	Volatility
SB fund	13.2%	16%
Gold	4.5%	25%
Correlation of gold with stock and bond portfolio	-0.20
Risk-free rate	2%

1. What new portfolio consisting of the SB fund along with gold would maximize the Sharpe ratio? You can use Excel solver and the following formulas from class: ; .

2. What portfolio would minimize risk for an expected return of 11%?

3. Your client thinks gold is a “safe” asset because it would be of value in the event of a global economic catastrophe and they might like to invest all of their money in it. In particular, your client is revealing that they are very risk averse. Would 100% gold be a wise strategy given their risk aversion?

Part 2:

You are a fixed income risk manager at a bank performing a scenario analysis. Your bank’s portfolio consists of 50% corporate bonds and 50% subprime mortgage-backed securities (MBS). You forecast the distributions of returns on these portfolios as described in the table below:

		Corporate bond portfolio	Subprime MBS portfolio
Scenario	Prob.	Return (%)	Return (%)
Severe recession	10%	-15%	-20%
Mild recession	20%	12%	6%
Normal growth	40%	10%	15%
Boom	30%	1%	10%

4. Due to regulatory requirements, your fixed income portfolio is not supposed to have losses of more than 15% or more with 10% or greater probability. Based on your forecasts, do you currently satisfy this requirement with your current portfolio? (Hint: no calculation is necessary)

5. Senior management is pressuring you to allow for more investment in subprime MBS, which have recently been highly profitable (and good for their bonuses). You counter that subprime MBS are too risky given your bank’s risk constraint. They argue that your portfolio is well-diversified given that it contains both corporate and mortgage-backed bonds and therefore it is not that risky to add more MBS.

1. Compute the correlation between the Corporate bond portfolio and the Subprime MBS portfolio.
2. Does this correlation suggest that the corporate bonds are a “good diversifier” for subprime MBS?s

Answer 1

Please note since there are multiple questions, I'll only be solving the Part I. Please post Part II seperately for the solution.

Answer with Explanation for Part 1 :

Step 1 : Maximize sharpe ratio- using the below table calculating the sharpe ratio with different combination of portfolio weights.

The results from the above table are as follows :

As per the table above the sharpe ratio is maximised at 0.74 using 80% of SB fund and 20% of gold in the portfolio.

Step 2 : Minimize risk of unexpected return

As per the above table, the porfolio that would minimize the risk at ~11% is using 70% of SB fund and 30% of gold in the portfolio.

Step 3 : Evaluate 100% of gold strategy in a portfolio

There is no such thing as a risk-free investment – all investments, including those that are guaranteed to return principal, carry some sort of risk.

An example of the risks involved in gold investments can be demonstrated by the following example, in the financial crisis of 2009, the value of gold increased many fold.

However in 2011, the gold prices reached roughly $2000 dollars an ounce, a rise of over $1000 in less than two years. recently the gold price are around  ~$1700, so if one would have bought gold around 2011 at its peak they would have definitely made losses over the years. As a result investing 100% of the portfolio might not be a good strategy for even a risk averse investor, a combination of both expected return and risk for diversified portfolio is always better.