In: Finance
Ravinder's Guitar Shop is expected to generate a 30% return in a boom market, a 15% return in a normal market, and a minus 25% (i.e. -25%) return in a recession. There is a 40% probability of a boom market, a 40% probability of a normal market and a 20% probability of a recession. What is (a) the expected return and (b) the standard deviation of Ravinder's Guitar Shop?
EXPECTED RETURN = 13%
STANDARD DEVIATION = 8.62%
RAVINDER GUITAR SHOP | ||
PROBABLITY | RETURN | |
BOOM | 0.4 | 30.0% |
NORMAL | 0.4 | 15.0% |
RECESSION | 0.2 | -25.0% |
SECURITY A | ||
EXPECTED RETURN | =(0.4x30)+(0.4x15)+(0.2x(-25)) | |
EXPECTED RETURN | 13.00% |
RAVINDER GUITAR SHOP | |||||
PROBABLITY | EARNINGS | return x | MEAN | return x - mean | (return-mean)^2*pr |
0.4 | 30% | 0.12 | 0.0433 | 0.077 | 0.00588 |
0.4 | 15% | 0.06 | 0.0433 | 0.017 | 0.00028 |
0.2 | -25% | -0.05 | 0.0433 | -0.093 | 0.00871 |
average return | 0.043333333 | =(0.12+0.06-0.05) / 3 | sum | 0.0149 | |
variance | =sum/n-1 | 0.007433333 | |||
std deviation | =(sum/n-1)^(1/2) | 0.086216781 |