Above are long term average annual returns for stocks bonds

Above are long -term average annual returns for stocks, bonds and cash and the standard deviations for those asset classes. (I\'ve rounded to ease your calculations.) investor loses money in any given year investing in only stocks ? Suppose I have a portfolio that has 1/3 of my assets in stocks ,1/3 in bonds and portfolio. You many assume the asset classes are independent. What is the probability that an investor loses money in any given year investing in the portfolio described in part b.

Solution

2. a.

When Return is less than 0% then, it will be in loss

Z = (0 – mean return)/Standard Deviation

Z = (0-10)/18 = -.5556

As per the Z table, Area= .2912

Thus,

Probability of Loss for stock = .2912

2.b.

Expected Mean return = 1/3*(10% +8%+6%) = 8%

Standard Deviation = (.33^2*18^2 + .33^2*7^2 + .33^2*3^2)^(1/2) = 6.449

Here, correlation among stock, bond and cash is zero as mentioned in the question)

2.c.

Z = (0-8) / 6.449 = -1.2405

At this z value, area = .1075

Thus, probability of loss at this portfolio = .1075