Question

the Capital Asset Pricing Model is a financial model that assumes returns on a portfolio are normally distributed. Suppose a portfolio has an average annual return of 14.7% (i.e. an average gain of 14.7%) with a standard deviation of 33%. A return of 0% means the value of the portfolio doesn't change, a negative return means that the portfolio loses money, and a positive return means that the portfolio gains money.

a.) What percent of years does this portfolio lose money, i.e. have a return less than 0%

b.) What is the cutoff for the highest 15% of annual returns with this portfolio

please shiw me how to out this on a TI83 caculator trying to learn it :)

Answer 1

Part a.

Let X be the random variable follows normal distribution with mean(μ) 14.7% and standard deviation(σ) 33%.

P(X<0) =P(X-μ/σ <0-14.7/33)

=P(Z<-0.45)

=0.3264 ========>>>Using Excel function ''=NORMSDIST(-0.45)''

The percent of the year’s portfolio lose money, that is have a return less than 0% is 32.64%.

Using TI-83:

Press 2^nd VARS [DISTR].

Scroll down to 2:normalcdf( and Press ENTER

Enter -9999,0,14.7,33)
and press ENTER
to get the answer .3264

.

Part b.

P(X>x)=0.15

1-P(X<=x)=0.15

P(X<=x)=1-0.15

P(X<=x)=0.85

P(Z<=1.04)=0.85 ======>>>> Uisng Excel function ''=NORMSINV(0.85)''

So z=1.04

x-μ/σ=1.04

x=μ+σ1.04

x=14.7+33*1.04

=49.02

The cutoff for the highest 15% of annual returns with this portfolio is 49%.

TI 83 Steps:

Press 2^nd VARS [DISTR].

Scroll down to

3:invnorm(0.85,14.7,33)

Press ENTER. You will get answer 48.9 means 49%

Hope this will be helpful. Thanks and God Bless You :)