# Finance forum post responses | Business & Finance

I need a 125 word reply to each of the following four forum post (500 words total):

See attached for a more readable copy of the forum post

Forum #1

(Posting early as I am in the process of moving and will not be readily accessible to the internet.)
1.      Use the following information on states of the economy and stock returns to calculate the expected return for Dingaling Telephone.
The expected return for Dingaling Telephone would be:
Recession – .30 x -.08 = -.024
Normal – .40 x .13 = .052
Boom – .30 x .23 = .069
Expected Return : -0.024 + 0.052 + 0.069 = 0.0970 or 9.7%.
2.      Using the Using the information in the previous question, calculate the standard deviation of returns.
To find the standard deviation I used excel to work out the equation, but in general form:
I took the values in security return column subtracted by the expected return squared, with the values in the probability column.
√((-.08, .13 and .23) – 0.097)2(.30, .40, .30) = 0.123048771 or 12.30%
My excel formula was: =SQRT(SUMPRODUCT((C1:C3-D5)^2,B1:B3))
3.      Repeat Questions 1 & 2 assuming that all three states are equally likely.
Expected Return would be 0.09324 or 9.32% and Standard deviation would be 0.129120942 or 12.91%. I completed both formulas in excel, but the general form would be similar to the previous problem but subbing in 0.333 for all the values in the Probability column rather than the .30, .40 and .30 that are currently there.
Jordan, B., Miller, T., & Dolvin, S. (2012). Fundamentals of investments, valuation and management (6th ed.). New York, NY:  McGraw-Hill. ISBN: 13: 9780073530710

Forum #2
A. Use the following information on states of the economy and stock returns to calculate the expected return for Dingaling Telephone.

State of Economy

Probability of State of the Economy

Security Return if State Occurs

Recession

.30

-8%

Normal

.40

13

Boom

.30

23

Recession = .30 X -8% = -0.024         Normal = .40 X 13% = 0.052
Boom = .30 X 23% = 0.069
Expected return = -0.024 + 0.052 + 0.069 = 0.097 or 9.7%
B. Using the information in the previous question, calculate the standard deviation of returns.
= (.30) X (-.08 – 0.097)2 + (.40) X (.13 – 0.097)2 + (.30) X (.23 – 0.097)2
= .0093987 + .0004356 + .0053067 = .015141
= √ .015141 = .12304 = 12.30%
C. Repeat Question 1 & 2 assuming that all three states are equally likely.
= .30 + .40 + .30 = 1.00/3 = .333
Recession = .333 X -8% = -0.02664   Normal = .333 X 13% = .04329
Boom = .333 X .23 = 0.07659
Expected return = -0.02664 + .04329 + 0.07659 = .09324 or 9.32%
Standard deviation or return –
= (.333) X (-.08 – .09324)2 + (.333) X (.13 – .09324)2 + (.333) X (.23 – .09324)2
= 0.009994028 + 0.000449982 + 0.006228198 = 0.016672208
= √0. 016672208 = 0.129120904 = 12.91%
Reference:
Jordan, B., Miller, T., & Dolvin, S. (2012). Fundamentals of investments, valuation and management (6th ed.). New York, NY:  McGraw-Hill. ISBN: 13: 9780073530710
Forum #3

a. What is the expected return on a portfolio that is equally invested in the two assets?
The expected return on a portfolio that is equally invested would be:
0.09 + 0.04 / 2 = 0.065 or 6.5%
b. If a portfolio of the two assets has a beta of .5, what are the portfolio weights?
The portfolio weights would be:
0.5 / 0.9 – 1 = 0.444444 or 44.44%
c. If a portfolio of the two assets has an expected return of 8 percent, what is its beta?
The beta would be:
0.8 x 0.9 = 0.72
d. If a portfolio of the two assets has a beta of 1.80, what are the portfolio weights? How do you interpret the weights for the two assets in this case? Explain.
The portfolio weights would be:
1.80 / 0.9 = 2
1-(1.80 / 0.9) = -1
The interpretation of the weights for the two assets would be that they seem to be over invested in stocks and in the negatives for the other which would be a risk free asset. The portfolio weight would represent that the stocks are over invested at 200% and -100% for risk free. For the risk free investment you could be borrowing at the risk free rate in order to buy more of that particular stock.

Forum #4

Complete Problem 10 from the Questions and Problems section of Chapter 12: A stock has a beta of .9 and an expected return of 9 percent. A risk-free asset currently earns 4 percent.
a. What is the expected return on a portfolio that is equally invested in the two assets?
Stock Expected return   = 0.09                         Beta    = 0.9
Bond Expected Return   = 0.04                        Beta    = 0.9
(.09 + .04) / 2   = .065 x 100
Expected Return = 6.50%
b. If a portfolio of the two assets has a beta of .5, what are the portfolio weights?
Stock Expected return   = 0.09                         Beta    = 0.5
Bond Expected Return   = 0.04                        Beta    = 0.5
(0.5 / 0.9) = .5555 -1 = .44444 x 100
Portfolio Weight = 44.44%
c. If a portfolio of the two assets has an expected return of 8 percent, what is its beta?
Stock Expected Return   = .08
Bond Expected Return   = .08
E(Rp)   =  .8 x 0.9
Beta   = .72
d. If a portfolio of the two assets has a beta of 1.80, what are the portfolio weights? How do you interpret the weights for the two assets in this case? Explain.
Stock Expected Return   =   .09              Beta    = 1.8
Bond Expected Return   =   .04               Beta    = 1.8
1.8 / .09   = .20 x 100
Stock Portfolio Weight = 2
1 – (1.8 / .09) = 1- 2 = -1
Bond Portfolio Weight = -1
The portfolio is currently over weighted in stocks and is under weighted in bonds.

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