Question

INVESTING YOUR OWN PORTFOLIO

You have won the jackpot of a European Lottery with a prize of €30 000. After distributing a portion of the prize to a local charity, you decide that it is a good idea to invest the rest of the prize. However, you are doubtful about which asset class or financial vehicle is more suitable given the current international context.

Bear in mind that you are in your early twenties and that your financial restrictions are negligible. While you are Not a Risk Lover, you feel comfortable with a portfolio with a high risk-reward profile. You seek professional advice and contact two recognized investment advisors.     

Investment Advice Summary

You had a virtual meeting with each of advisor and then you summed-up their financial advices as follows:

	Advisor 1	Advisor 2
Percentage invested in Bonds	85%	40%
Percentage invested in Equity	15%	60%
Investment Vehicle	Mutual Funds	Exchange Traded Funds (ETF)
Geographic Exposure	European Funds only	Global ETFs
Currency Exposure	Unhedged	80% FX-hedging into your local currency
Liquidity	Low to Moderate	High
Portfolio management style	Active	Passive
Rebalancing Frequency	Every six months	Every two years

3- Capital Allocation Line (CAL):

After a few of weeks of deliberation, you made-up your mind and you selected an advisor, who is not any of the advisors that you initially interviewed. In a follow-up email, you learned that most of your portfolio is invested in a risky asset (global megatrends equity ETF) with an expected rate of return of 13% and standard deviation of 19%. The relevant risk-free rate is 2%. (4 points each question; total of 20 points)

1. The strategic asset allocation of your portfolio is 70% in a global equity ETF and 30% in a risk-free money market fund. What is the expected return on your portfolio?
2. Which is the standard deviation of the rate of return on your portfolio?
3. What is the reward-to-volatility ratio (Sharpe ratio) of the global equity ETF? Which is the Sharpe ratio of your portfolio?
4. Imagine that you want to draw a Capital Allocation Line (CAL) with these data, which is the value of its intercept? Which would be its slope?
5. If the risk-free rate were to increase to 5%, what would happen to CAL that you have drawn?

Answer 1

1.) Expected return on the portfolio = Er(security 1)*W1 + Er(security 2)*W2
= 13%*70% + 2%*30%
= 9.7%
where, security 1 is global megatrends equity ETF and security 2 is risk-free money market fund
W1 is the weight of amount invested in security 1 and W2 is weight of amount invested in security 2

2.) Portfolio risk (Standard Deviation of portfolio) =
=

= 13.3%
where SD1 is standard deviation of security 1 and SD2 is standard deviation of security 2 and R12 is correlation between two securities.

3.) Sharpe Ratio (Global equity ETF) = Er - Rf / Risk of security
= 13%-2% / 19%
= 0.58

Sharpe Ratio (Portfolio) = E(r) - Rf / Risk of portfolio
= 9.7% - 2% / 13.3%
= 0.58

4.) Equation of CAL - Er (portfolio) = Rf + Sharpe Ratio* Risk(Portfolio)
Therefore, slope of line = Sharpe Ratio = 0.58
Intercept (Y) = Rf = 2%
Intercept (X) = -Rf / Sharpe Ratio
= -2% / 0.58
= -3.45%

5.) If Risk-free rate increases to 5%, CAL will shift upward and become more steep.
Y intercept will increase to 5% and X intercept will change to - 11.9%
Sharpe ratio = 0.42

Note - Expected portfolio return will change to 10.6%, thus sharpe ratio will change to 0.42