Question

You bought an investment portfolio of 300 shares of xzy company and 700 share OZ Company (5) years ago with total investment of $100,000. Today you can sell XZY for $125/share and OZ for 155/share. XZY paid dividend $13.5/share per year and oz paid $18.5/share as its dividend each year. The following is the next year forecast relates to this portfolio. State of economy Probability of economic state Rate of return Boom 0.35 17% Normal 0.55 13% Recession 0.10 -6% Required: 1) Calculate your dividend income and capital gain from this portfolio if you decide to sell all the shares? 2) Calculate the expected return of the portfolio for the next year 3) Determine the risk of the portfolio by computing portfolio standard deviation

Answer 1

Part 1)

Step 1: Calculate Purchase Value of Each Company's Stock

We have not been given the purchase price in the question. Therefore, we will take the proportion of investment (on the basis of number of shares in each company) as the basis for arriving at purchase value of each company's stock as below:

Total Investment Value in Dollars = $100,000

Purchase Value of XZY Company's Stock = Total Investment Value in Dollars*Number of XZY Shares/Total Shares Acquired = 100,000*300/1,000 = $30,000

Purchase Value of OZ Company's Stock = Total Investment Value in Dollars*Number of OZ Shares/Total Shares Acquired = 100,000*700/1,000 = $70,000

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Step 2: Calculate Dividend Income and Capital Gain

The value of dividend income and capital gain is arrived as follows:

Dividend Income (XZY Company's Stock) = Total Shares Acquired*Dividend Per Share*Number of Years = 300*13.5*5 = $20,250

Dividend Income (OZ Company's Stock) = Total Shares Acquired*Dividend Per Share*Number of Years = 700*18.5*5 = $64,750

Capital Gain (XZY Company's Stock) = Sales Value - Purchase Value = 300*125 - 30,000 = $7,500

Capital Gain (OZ Company's Stock) = Sales Value - Purchase Value = 700*155 - 70,000 = $38,500

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Tabular Representation

	XZY	OZ
Dividend Income	$20,250	$64,750
Capital Gain	$7,500	$38,500

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Part 2)

The expected return of the portfolio for the next year is determined as follows:

Expected Return of Portfolio = Probability of Boom Economic State*Return of Return under Boom Economic State + Probability of Normal Economic State*Return of Return under Normal Economic State + Probability of Recession Economic State*Return of Return under Recession Economic State

Substituting values in the above formula, we get,

Expected Return of Portfolio = .35*17% + .55*13% + .10*(-6%) = 12.50%

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Part 3)

Step 1: Calculate Variance of Portfolio

The variance of the portfolio can be calculated with the use of following formula:

Variance = Probability of Boom Economic State*(Return of Return under Boom Economic State - Expected Return of Portfolio)^2 + Probability of Normal Economic State*(Return of Return under Normal Economic State - Expected Return of Portfolio)^2 + Probability of Recession Economic State*(Return of Return under Recession Economic State - Expected Return of Portfolio)^2

Substituting values in the above formula, we get,

Variance = .35*(17% - 12.50%)^2 + .55*(13% - 12.50%)^2 + 10%*(-6% - 12.50%)^2 = 0.004145

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Step 2: Calculate Standard Deviation of Portfolio

The value of standard deviation of portfolio is calculated as follows:

Standard Deviation of Portfolio = (Variance)^1/2 = (0.004145)^1/2 = 0.06438 or 6.44%