Question
In: Finance
1. The following forecasts are available for the state of the economy and for two securities:...
| 1. The following forecasts are available for the state of the economy and for two securities: | ||||||||
| a. Compute the two stocks expected return, variance, standard deviation, covariance and correlation. | ||||||||
| b. Create a portfolio 30% in High Tech (remainder in Low Tech); calculate the portfolio expected return and standard deviation. Compare and discuss these results to Low Tech stand- alone results. | ||||||||
|
State of the Economy |
Probability of State Occurring | Return on High Tech Asset (%) | Return on Low Tech Asset (%) | |||||
| Severe Recession | 25.00% | -30.00% | 0.00% | |||||
| Recession | 25.00% | -10.00% | 8.00% | |||||
| Normal Growth | 25.00% | 30.00% | 12.00% | |||||
| Boom | 25.00% | 50.00% | 8.00% | |||||
Solutions
Expert Solution
a).
| State of the Economy | Probability of State Occurring (P) | Return
on High Tech Asset (%) (Rht) |
Probability weighted return for High Tech Asset (P*Rht) |
P*(Rht-E(Rht))^2 |
| Severe Recession | 25.00% | -30.00% | -7.50% | 0.0400 |
| Recession | 25.00% | -10.00% | -2.50% | 0.0100 |
| Normal Growth | 25.00% | 30.00% | 7.50% | 0.0100 |
| Boom | 25.00% | 50.00% | 12.50% | 0.0400 |
| E(Rht) | 10.00% | |||
| Variance (∑(P*(Rlt-E(Rlt))^2)) | 0.100000 | |||
| Stdev (Variance^0.5) | 0.316228 |
| State of the Economy | Probability of State Occurring (P) | Return
on Low Tech Asset (%) (Rlt) |
Probability weighted return for Low Tech Asset (P*Rlt) |
P*(Rlt-E(Rlt))^2 | P*((Rht-E(Rht)*(Rlt-E(Rlt)) |
| Severe Recession | 25.00% | 0.00% | 0.00% | 0.0012 | 0.0070 |
| Recession | 25.00% | 8.00% | 2.00% | 0.0000 | (0.0005) |
| Normal Growth | 25.00% | 12.00% | 3.00% | 0.0006 | 0.0025 |
| Boom | 25.00% | 8.00% | 2.00% | 0.0000 | 0.0010 |
| E(Rlt) | 7.00% | Covariance (∑P*((Rht-E(Rht)*(Rlt-E(Rlt))) | |||
| Variance (∑(P*(Rlt-E(Rlt))^2)) | 0.001900 | 0.010000 | |||
| Stdev (Variance^0.5) | 0.043589 |
Correlation = Covariance/StdevHT*StdevLT
= 0.0100/(0.316228*0.043589) = 72.55% (or 0.725476)
b). Portfolio expected return = (WHT*E(RHT))+(WLT*E(RLT))
= (0.3*10%)+(0.7*7%) = 7.90%
Portfolio standard deviation = [(WHT*StDevHT)^2 + (WLT*StDevLT)^2 + (2*WHT*WLT*Covariance)]^0.5
= [(0.3*0.316228)^2 + (0.7*0.043589)^2 + (2*0.3*0.7*0.01)]^0.5 = 0.1189
Compared to Low Tech stock, the portfolio has higher expected return but the riskiness has increased a bit.
jeff jeffy answered 11 months agoRelated Solutions
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