Discrete and Continuous Random Variables Exercise

*** Shouldn’t take too long as it can be solved with some excel formulas and brief explanation of answers + definition of concepts would be required

Questions:

For each investment class in Table 3, assume that future returns are normally distributed with the population mean and standard deviation as given. Answer the next 5 questions

Tutorial video for excel formula: https://www.viddler.com/embed/ebd96754

Based on this assumption:

1. 1)For each investment class, find the probability of a return that is less than zero (that is, find the probability of a loss). Is your answer reasonable for all investment classes? Explain. 
2. 2)For each investment class, find the probability of a return that is: 
   1. Greater than 5%.
   2. Greater than 10%. 
   3. Greater than 20%. 
   4. Greater than 50%. 

Fixed Annuities

Cash Equivalents

US Treasury Bonds

US Investment-grade Corporate Bonds

Non US Corporate Bonds

Domestic Large Cap Stocks

International Equities

Domestic Mid Cap Stocks

Domestic Small Cap Stocks

P(x>5%)

P(x>10%)

P(x>20%)

P(x>50%)

1. 3)For which investment classes is the probability of the return greater than 50% is essentially zero? For which investment classes is the probability of such a return greater than 1 percent? Greater than 5%? 
2. 4)For which investment classes is the probability of loss essentially zero? 
3. 5)For which investment classes is the probability of loss greater than 1%? Greater than 10%? Greater than 20%?

Table 3

Data on Rate of Return of Investment in Securities

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