You invest in a stock with the following probability distribution of returns: A

Question

You invest in a stock with the following probability distribution of returns:

A probability of .15 that the return will be 16%; a probability of .35 that the return will be 24%; a probability of .3 that the return will be -40%; and a probability of .2 that the return will be 45%.

Based on this data and assuming the stock returns are normally distributed, you can say with a probability of 95% that the actual return will be in the range of?

You invest in a stock with the following probability distribution of returns:

A probability of .15 that the return will be 16%; a probability of .35 that the return will be 24%; a probability of .3 that the return will be -40%; and a probability of .2 that the return will be 45%.

Based on this data and assuming the stock returns are normally distributed, you can say with a probability of 95% that the actual return will be in the range of?

Explanation / Answer

Expected Return = 0.15*16% +0.35*24% + 0.3*-40% + 0.2*45%

Expected Return = 7.80%

Standard Deviation = (0.15*(16%-7.80%)^2 +0.35*(24%-7.80%)^2 + 0.3*(-40%-7.80%)^2 + 0.2*(45%-7.80%)^2)^(1/2)

Standard Deviation = 32.62%

Using Excel Formula

Z = NORMSINV(95%)

Z = 1.64485

Upper limit of actual return of Range = z*Sd + Expected Return

Upper limit of actual return of Range = 1.64485*32.62% + 7.80%

Upper limit of actual return of Range = 61.46%

Lower limit of actual return of Range = Expected Return -  z*Sd

Lower limit of actual return of Range = 7.80%- 1.64485*32.62%

Lower limit of actual return of Range = - 45.86%

Based on this data and assuming the stock returns are normally distributed, you can say with a probability of 95% that the actual return will be in the range of: -45.86% to 61.46%

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