Final answer:
To compare the two investment strategies, one can calculate the expected outcomes of each and derive the standard deviation to understand the risk associated with each one. The first strategy results in a straightforward 30% standard deviation for the second year's market investment, while the second strategy requires a more complex calculation considering the compounded effects over two years.
Step-by-step explanation:
A student asked about comparing two investment strategies with a risk-free interest rate of 5% and a stock market that can return either 40% or -20%. We aim to compute the standard deviation for each case. For strategy B (1), investing one year in the risk-free investment and then one year in the market, the return will be straightforward. The first year will yield 5%, while the second year's return will be either 40% or -20% due to the stock's unpredictable nature. For strategy B (2), which involves investing in the market for both years, the potential outcomes are 40% both years, 40% the first year and -20% the second, -20% the first year and 40% the second, or -20% both years.
To calculate the standard deviation, we first need the expected value (mean) of the returns. Then, we calculate the variance by finding the squared difference from the mean for each outcome and taking the expected value. Finally, we take the square root of this variance to get the standard deviation.
For B (1), if we assume the risk-free rate occurs in the first year and the stock market in the second, we only need to find the variance of the stock market year, as the risk-free year has a guaranteed return. In this case, the expected value (mean) for the second year is the average of 40% and -20%, which is 10%. The variance for the second year is then the average of the squared differences from the mean, ((40-10)^2 + (-20-10)^2) / 2. Calculating this gives a variance of 900; therefore, the standard deviation is the square root of 900, which is 30%.
For B (2), we have four scenarios for returns over two years compounded. With equal probability, we would calculate the mean and then find the variance of these outcomes, considering compounding effect (1 + return year 1) * (1 + return year 2) - 1. The formula for variance would incorporate the probabilities and the squared deviations from this mean. Finally, we would again take the square root of this variance to obtain the standard deviation for the two-year market investment.
Investment risk and standard deviation are crucial components of financial decision-making and can help investors understand the potential volatility and returns associated with different investment strategies.