Question

Planning for the Future

Ayasha, age 30, is beginning to contemplate her financial future.  Right now, she lives in a large city where she rents a one-bedroom apartment. Although she loves the excitement of the city, she knows that someday she would like to move to the country and live in a farmhouse. Her goal is to begin saving for this objective right away.  Ayasha has indentified three possible portfolios that might be appropriate choices as she begins investing to reach her objective.  Each portfolio consists of the following stocks, bonds, and cash assets.

Portfolio 1                                Portfolio 2                                Portfolio 3

10% cash                                  10% cash                                  15% cash

20% bonds                                40% bonds                                50% bonds

70% stocks                                50% stocks                                35% stocks

Instructions

1. Calculate the weighted average rate of return for each portfolio, assuming that the average return of each asset is as follows.  (Hint:  Multiply the allocation percentage by the rate of return to determine the “weighted average” for the asset: stocks 9%, bonds 4%, and cash assets 2%)
2. Which portfolio has the greatest level of uncertainty associated with the returns?  How can you tell?
3. If Ayasha’s risk tolerance is below average and she has a long-time horizon (15 years), which of the three portfolios would be most appropriate for her?
4. If Ayasha’s time horizon for goal achievement is 4 years, which portfolio would be most appropriate?
5. What type of risk does Ayasha face if she invests in portfolio 3?

Answer 1

a. weighted average rate of return = weight of asset*return of asset

weighted average rate of return portfolio 1 = (0.10*2%) + (0.20*4%) + (0.70*9%) = 0.2‬% + 0.8% + 6.3‬% = 7.3‬%

weighted average rate of return portfolio 2 = (0.10*2%) + (0.40*4%) + (0.50*9%) = 0.2‬% + 1.6‬% + 4.5‬% = 6.3‬%

weighted average rate of return portfolio 3 = (0.15*2%) + (0.50*4%) + (0.35*9%) = 0.3% + 2‬% + 3.15‬% = 5.45‬‬%

b. portfolio 1 has the greatest level of uncertainty associated with the returns because it has highest weight of 70% of stocks in the portfolio among all the portfolios. stock returns are more volatile and uncertain than bond and cash returns.

c. If Ayasha’s risk tolerance is below average and she has a long-time horizon (15 years), then portfolio 3 would be most appropriate for her because it has 65% of low risk assets (bond + cash) in the portfolio and 35% high risk asset (stock) which will help her get higher return compared to other 2 assets in the long-time horizon (15 years).

d. If Ayasha’s time horizon for goal achievement is 4 years, then portfolio 1 would be most appropriate because it has highest weight of 70% in the portfolio among all the portfolios. stock gives the higher return with higher risk compared to other 2 assets. if time horizon for goal achievement is short-term then higher weight in stocks can help in goal achievement.

e. Ayasha faces risk of not achieving her goal if she invests in portfolio 3 because 65% of portfolio is invested in low risk-low return assets. so it might be possible that she might not achieve her goal. she also faces interest rate risk. interest rate risk is the risk of decline in bond values when interest rates rise. so, this may also lead to not achieve her goal as 50% of portfolio is invested in bonds.