An investor has $20,000 to invest in stocks. She can buy blue chip or specu-
lative stocks. If the market goes up the blue chips will pay o® $30,000 and speculative will
pay o® $50,000. If the market goes down, the blue chips will pay o® $10,000 and speculative
will pay o® $1,000. If the probability of the market going up is :4, then the expected pro¯t
for the best strategy is closest to?
To find the expected profit for the best strategy, we can calculate the expected value by multiplying the payoff of each outcome by its respective probability and summing them up.
Let's consider the two strategies: investing the entire $20,000 in blue chip stocks or investing the entire $20,000 in speculative stocks.
For the blue chip strategy:
- If the market goes up (probability 0.4), the payoff is $30,000.
- If the market goes down (probability 0.6), the payoff is $10,000.
The expected value for the blue chip strategy is:
Expected Value = (0.4 * $30,000) + (0.6 * $10,000)
Expected Value = $12,000 + $6,000
Expected Value = $18,000
For the speculative strategy:
- If the market goes up (probability 0.4), the payoff is $50,000.
- If the market goes down (probability 0.6), the payoff is $1,000.
The expected value for the speculative strategy is:
Expected Value = (0.4 * $50,000) + (0.6 * $1,000)
Expected Value = $20,000 + $600
Expected Value = $20,600
Comparing the expected values, we see that the expected profit for the best strategy is closest to $20,600.
Therefore, the investor should invest the entire $20,000 in speculative stocks to maximize the expected profit.