Question

Example [15 marks in total] Portfolio X, a CPPI portfolio, has a floor value of $8.0 million, a market value of $10 million, and a multiplier of 2.5. The portfolio is rebalanced annually. a) In the first year, stocks increase by 20% and bonds decrease by 10%. In the second year, stocks decrease by 10% and bonds increase by 5%. Determine the amount of investment for stocks and bonds respectively for Portfolio X at the end of second year after rebalancing. [6 marks] Portfolio Y, a constant mix strategy of 50% stocks and 50% bonds, has a market value of $10 million. This portfolio is also rebalanced annually. b) Similar to a) above, stocks increase by 20% and bonds decrease by 10% in the first year. Then stocks decrease by 10% and bonds increase by 5% in the second year. Determine the amount of investment for stocks and bonds respectively for Portfolio Y at the end of second year after rebalancing. [6 marks] c) Comment on the relative performance of the CPPI and constant mix strategies in a) and b) and explain why. [3 marks]

Answer 1

a) At the end of the first year, the market value of Portfolio X will be $12 million (20% increase in stocks and 10% decrease in bonds). Since the floor value is $8 million, the cushion is $4 million. The investment in stocks will be $10 million - $8 million = $2 million. The investment in bonds will be ($4 million / 2.5) = $1.6 million. Therefore, the total investment in stocks and bonds respectively will be $4.6 million and $1.6 million.

At the end of the second year, the market value of Portfolio X will be $10.8 million (10% decrease in stocks and 5% increase in bonds). Since the floor value is $8 million, the cushion is $2.8 million. The investment in stocks will be ($10.8 million - $8 million) / 2.5 = $1.12 million. The investment in bonds will be $2.8 million - $1.12 million = $1.68 million. Therefore, the total investment in stocks and bonds respectively will be $2.72 million and $1.68 million.

b) At the end of the first year, the market value of Portfolio Y will be $9 million (20% increase in stocks and 10% decrease in bonds). Since the constant mix strategy is 50% stocks and 50% bonds, the investment in each asset class will be $4.5 million.

At the end of the second year, the market value of Portfolio Y will be $9.45 million (10% decrease in stocks and 5% increase in bonds). Since the constant mix strategy is 50% stocks and 50% bonds, the investment in each asset class will still be $4.725 million.

c) In both years, Portfolio X outperformed Portfolio Y. This is because CPPI allows for more upside potential when markets are rising, while still providing downside protection through the floor value. On the other hand, constant mix strategy maintains a fixed allocation to each asset class, which can limit potential gains in rising markets and may not provide enough downside protection in falling markets. However, CPPI can also lead to higher transaction costs due to the need for frequent rebalancing, while constant mix strategy may require less frequent rebalancing and lower transaction costs.