Question

Historically, the one-year returns follow approximately the normal distribution. The one-year return for the S&P 500 was +27% (that is, 0.27) and its standard deviation is 20% (that is, 0.2). What is the probability that a stock in the S&P 500 gained 30% or more last year?

Answer 1

To find the probability that a stock in the S&P 500 gained 30% or more last year, we can use the z-score and standard normal distribution table.

Step-by-step explanation:

To find the probability that a stock in the S&P 500 gained 30% or more last year, we need to calculate the z-score and use the standard normal distribution table. The z-score can be calculated using the formula:

z = (x - μ) / σ

where x is the value of the return we are interested in, μ is the mean of the returns, and σ is the standard deviation of the returns. In this case, x = 0.3 (30% gain), μ = 0.27, and σ = 0.2. Plugging these values into the formula, we get:

z = (0.3 - 0.27) / 0.2 = 0.15

Next, we look up the corresponding area under the standard normal distribution curve for the z-score of 0.15. From the table, we find that the area is approximately 0.5596. This represents the probability that a stock in the S&P 500 gained 30% or more last year.