Question

(Expected rate of return and risk)

B. J. Gautney Enterprises is evaluating a security.  One-year Treasury bills are currently paying 4.6 percent. Calculate the investment's expected return and its standard deviation. Should Gautney invest in this security?

Probability	Return
0.05	−5	%
0.35	1	%
0.55	6	%
0.05	9	%

Answer 1

Solution:

Calculation of  investment's expected return

Probability(P)	Return(R)	Expected Return(P*R)
0.05	-5%	-0.25%
0.35	1%	0.35%
0.55	6%	3.3%
0.05	9%	0.45%
Expected return		3.85%

Thus,investment's expected return is 3.85%.

b)Calculation of investment's standard deviation:

Standard Deviation=SQRT[Sum of (R-Expected return)^2*P]

=SQRT[(-5-3.85)^2*0.05+(1-3.85)^2*0.35+(6-3.85)^2*0.55+(09-3.85)^2*0.05]

=SQRT[10.6275]

=3.26%

c)Since,return on risk free asset(4.6%) is higher than the return of investment(3.85%),hence Gautney should not invest in this​ security.