Question

many investment decisions depend on a stocks performance relative to its own history. here are some summary statistics about the closing prices of two stocks over the past year:

stock mean standard deviation
stock a $mu = \\$4$ $sigma = \\$0.50$
stock b $mu = \\$32$ $sigma = \\$5.75$

today, eduardo bought shares at their closing prices in stock a for $4.75 each, while he bought shares in stock b for $28.50 each.

for which stock did eduardo pay less, relative to its previous prices?

choose 1 answer:

Explanation:

Step1: Calculate z - score for Stock A

The z - score formula is $z=\frac{x-\mu}{\sigma}$. For Stock A, $x = 4.75$, $\mu=4$, $\sigma = 0.50$. So $z_A=\frac{4.75 - 4}{0.50}=\frac{0.75}{0.50}=1.5$.

Step2: Calculate z - score for Stock B

For Stock B, $x = 28.50$, $\mu = 32$, $\sigma=5.75$. So $z_B=\frac{28.50 - 32}{5.75}=\frac{- 3.5}{5.75}\approx - 0.61$.

Step3: Compare z - scores

A lower z - score indicates that the price paid is lower relative to the stock's historical prices. Since $z_B\lt z_A$, Stock B has a lower z - score.

Answer:

Stock B