Constant mix portfolio: After the 10% decrease in the market, the portfolio consists of $2,500 in cash and 0.9 x $7,500 = $6,750 in stock, for a total value of $9,250. This represents a stock/total asset ratio of 6,750/9,250 = 0.7297. To maintain the desired 0.75 stock/total asset mix, additional stock must be purchased. The amount of stock that must be repurchased is determined as follows:

($6,750 + X)/$9,250 = 0.75, or X = $187.50.

After the purchase of $187.50 in additional stock, the portfolio consists of stock valued at $6,937.50 = $6,750 + $187.50 and cash in the amount of $2,500 – $187.50 = $2,312.50. Following the 11.11% increase in the stock market, the constant mix portfolio value is equal to:

$2,312.50 + 1.1111($6,937.50) = $10,020.83.

Thus, the ending value of the constant mix portfolio is $20.83 greater than that of the buy-and-hold portfolio. This demonstrates that a constant mix strategy outperforms a buy-and-hold strategy in a flat, oscillating market.