Question

The return of a portfolio is normally distributed with a mean return of 8% and risk of 10%. What is the probability that this portfolio's return is between 18% and 27.6%?

Answer 1

We will use the normal distribution tabes to find the probability of portfolio return between 18% and 27.6%.

But since this is not a standard normal distribution, we first need to transform it into standard normal distribution, before we can calculate the probability using tables.

Now, in our question,

Z₁ = (18% - 8%)/10% = 1

Z₂ = (27.6% - 8%)/10% = 1.96

Now, this is how our diagram would look like

This is how, diagramatically our question looks and we need to calculate the probability within the shaded ragion (in red).

Over here, we would first calculate the probability of Z1 > 1 and substract the probability of Z2>1.96 to get the shaded region probability. You need to look at Z-tables for finding this probability

P (Z1 > 1) = 0.50 - 0.3413 = 0.1587 (Since only 50% probability lies on one side of axis in a normal distribution)

P(Z2 > 1.96) = 0.50 - 0.4750 = 0.025

P(required) = 0.1587 - 0.025 = 0.1337 = 13.37%

(Please mention in comment if you are not aware of how to look at the Z-tables)