calculate the expected return

Question

1. Calculate the expected return on an asset that has the following probable
returns:
Order Return (%) Probability
1 634 .39
2 814 .27
3 912 .19
4 7% . 09
5 4% . 06












2. If you compare the asset in Exercise 1 to the following asset, can you quickly
tell which one is riskier?

Order Return (%) Probability
1 9% .29
2 10% .25
3 612% .22
4 5% .15
5 4% .09























3. If these two assets are in the same portfolio, would that be better or worse for the portfolio return? Can you tell by a quick examination, and how?
































4. Calculate the standard deviation of the two assets in Exercises 1 and 2 and explain how you can use the standard deviation to tell which asset is riskier.

























5. Calculate the coefficient of variation of the two assets in Exercises 1 and 2
and explain which asset is riskier, and why.




























6. Calculate the portfolio return of the following five-asset portfolio and how
they are making up the portfolio capital.
Asset Return (%) Asset % of Portfolio
A 14% .25
B 1312% .20
C 12% .15
D 914% .26
E 10% .14




















7. Calculate the portfolio return for a business whose market value went up from $720000 in 2010 to $985000 in 2011.

Answer 1

1. The formula for Expected Return is P*R, where P = probability and R = return. 

 

2. Investments with a lower probability of a  return are riskier. Example:

 

Case 1

Probability = .5

Return = 400%

-------------------

Expected Return = .5*400% = 200%

 

Case 2

Probability = .01

Return = 20000%

-------------------

Expected Return = .01*20000% = 200%

 

 

Even though they have the same Expected Return, obviously Case 2 is more risky because chances of winning are very low. Its like the lottery. Case 1, on the other hand, is closer to a sure thing but for lower return. 

 

Answer 2

To compute statistics given returns and probabilites, put the returns in one list in your calculator and the probabilities in another. Using the 1-var stat function, specify the list with the returns as data and the list with probabilities as the frequency.

 

1. Expected return (mean) = 6.4119 (Note these seem like unrealistic returns given in the problem.)

    The standard deviation is 2.8736

 

2. Expected return = 1.4086

    The standard deviation is 2.5022

 

3. I still don't understand this question. See my previous post.

 

4. see above. Asset 1 has the higher standard deviation and is riskier.

 

5. coefficient of variation = standard deviation/mean

    Asset 1: 2.8736/6.4119 = 0.4482

    Asset 2: 2.5022/1.4086 = 1.7764

    This reveals that Asset 2 is riskier relative to its return. In other words, compared to Asset 2, Asset 1     is worth the risk.

 

6. Using the same calculator procedure. I get the mean to be 506.7%

    I don't understand the second part of the question. The allocation of capital is given by the % of portfolio.

 

7.  (985,000-720,000)/720,000 = 36.8%