Question

Consider the following information about Stocks I and II: Rate of Return If State Occurs State of Probability of Economy State of Economy Stock I Stock II Recession .20 .09 −.26 Normal .60 .18 .13 Irrational exuberance .20 .12 .46 The market risk premium is 5 percent, and the risk-free rate is 4 percent. (Do not round intermediate calculations. Round your answers to 2 decimal places, e.g., 32.16. Enter your return answers as a percent. ) The standard deviation on Stock I's return is ---------percent, and the Stock I beta is -------. The standard deviation on Stock II's return is ------percent, and the Stock II beta is --------. Therefore, based on the stock's systematic risk/beta, Stock is 1 "riskier".

Answer 1

The student's question related to the standard deviation and beta of two stocks is focused on assessing risk and estimating returns, reflecting the finance and investment concepts taught in a college-level business course.

Step-by-step explanation:

The student is asking about the calculation of standard deviation and beta for two different stocks based on their returns given different states of the economy. This type of problem is found in finance and investment courses, typically taught at the college level.

Identifying which stock is riskier involves comparing the beta of each stock. The beta measures a stock's volatility relative to the market. A higher beta indicates a stock is more volatile and therefore riskier compared to the market.

Risk refers to the uncertainty and the potential range of outcomes for an investment return, while expected rate of return is an average measure of the profitability over time. Additionally, actual rate of return is what the investor actually realizes on their investment and includes both capital gains and income from dividends or interest. These concepts are central to understanding the trade-off between risk and potential rewards in investing.

Answer 2

The standard deviation of Stock I's return is approximately 33.30%.
- The standard deviation of Stock II's return is approximately 50.65%.

To calculate the standard deviation of Stock I's return, we need to use the formula:

Standard deviation = √[ ∑ (Ri - Rm)^2 * Pi ]

Where:
- Ri is the return on Stock I in a specific state of the economy
- Rm is the average return on Stock I in all states of the economy
- Pi is the probability of each state of the economy

Using the given data, we can calculate the standard deviation of Stock I's return as follows:

Recession: (0.09 - 0.04)^2 * 0.20 = 0.00025
Normal: (0.18 - 0.04)^2 * 0.60 = 0.10080
Irrational exuberance: (0.12 - 0.04)^2 * 0.20 = 0.00960

Summing up these values: 0.00025 + 0.10080 + 0.00960 = 0.11065

Taking the square root of this sum: √0.11065 ≈ 0.3330

So, the standard deviation of Stock I's return is approximately 0.3330, or 33.30%.

To calculate the beta of Stock I, we need to use the formula:

Beta = Covariance(Stock I, Market) / Variance(Market)

The covariance of Stock I and the market is not given, so we cannot calculate the beta.

Moving on to Stock II, we can calculate its standard deviation using the same formula as above. Using the given data, we have:

Recession: (0.26 - 0.04)^2 * 0.20 = 0.04544
Normal: (0.13 - 0.04)^2 * 0.60 = 0.03816
Irrational exuberance: (0.46 - 0.04)^2 * 0.20 = 0.17296

Summing up these values: 0.04544 + 0.03816 + 0.17296 = 0.25656

Taking the square root of this sum: √0.25656 ≈ 0.5065

So, the standard deviation of Stock II's return is approximately 0.5065, or 50.65%.

The beta of Stock II is not given, so we cannot calculate it.

Since we do not have the beta values for both stocks, we cannot determine which stock is riskier based on systematic risk/beta.