Scenario Analysis and Portfolio Risk. The common stock of Leaning Tower of Pita Inc., a restaurant chain, will generate payoffs to investors next year, which depend on the state of the economy, as follows: ( LO11-2 and 2011-3)
90 Normal economy
| Dividend | Stock Price | |
| Boom | $8 | $240 |
| Normal economy | 4 | 90 |
| Recession | 0 | 0 |
a. The company goes out of business if a recession hits. Calculate the expected rate of return and standard deviation of return to Leaning Tower of Pita shareholders. Assume for simplicity that the three possible states of the economy are equally likely. The stock is selling today for $80.
a
Return in boom
| rate of return/HPR = ((Ending price+Dividend)/Beginning price-1) |
| =((240+8)/80-1) |
| =210% |
Return in normal economy
| rate of return/HPR = ((Ending price+Dividend)/Beginning price-1) |
| =((90+4)/80-1) |
| =17.5% |
| Stock | |||||
| Scenario | Probability | Return% | =rate of return% * probability | Actual return -expected return(A)% | (A)^2* probability |
| Recession | 0.3333 | 0 | 0 | -75.82575 | 0.191632314 |
| Normal | 0.3333 | 17.5 | 5.83275 | -58.32575 | 0.113385097 |
| Boom | 0.3333 | 210 | 69.993 | 134.17425 | 0.60003097 |
| 0 | 0 | 0 | -75.82575 | 0 | |
| Expected return %= | sum of weighted return = | 75.83 | Sum=Variance Stock= | 0.90505 | |
| Standard deviation of Stock% | =(Variance)^(1/2) | 95.13 | |||
Return in recession
| rate of return/HPR = ((Ending price+Dividend)/Beginning price-1) |
| =((0+0)/80-1) |
| =-100% |
The company goes out of business if a recession hits. Calculate the expected rate of return and standard deviation of return to Leaning Tower of Pita shareholders. Assume for simplicity that the three possible states of the economy are equally likely. The