Question

Assume the portfolio mean return is 10 percent and the standard deviation of return estimate is 20 percent per year. you want to calculate the following probabilities, assuming that a normal distribution describes returns.

A. What is the probability that portfolio return will exceed 20 percent?

B. What is the probability that portfolio return will be between 12 percent and 20 percent? in other words, what is P(12% ≤ Portfolio return ≤ 20%)?

C. You can buy a one-year t-bill that yields 5.5 percent. This yield is effectively a one- year risk-free interest rate. What is the probability that your portfolio’s return will be equal to or less than the risk-free rate?

Answer 1

USING z-TABLES
1.
Pr(X>20%)
=Pr(Z>(20%-10%)/20%)
=Pr(Z>0.5)
=1-Pr(Z<0.5)
=0.308537538725987

2.
Pr(12%<X<20%)
=Pr((12%-10%)/20%<Z<(20%-10%)/20%)
=Pr(0.1<Z<0.5)
=Pr(Z<0.5)-Pr(Z<0.1)
=0.151634623996984

3.
Pr(X<=5.5%)
=Pr(X<=(5.5%-10%)/20%)
=Pr(Z<=-0.225)
=0.41098963713127

USING EXCEL
1.
=1-NORMDIST(20%,10%,20%,TRUE)=0.308537538725987

2.
=NORMDIST(20%,10%,20%,TRUE)-NORMDIST(12%,10%,20%,TRUE)=0.151634623996984

3.
=NORMDIST(5.5%,10%,20%,TRUE)=0.41098963713127