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LerDarreus Young

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Chapter 7
"Mini-Case"

Scenario
As a first day intern at Tri-Star Management Inc., the CEO asks you to analyze the following information pertaining to two common stock investments: Tech.com and Sam’s Grocery. You are told that a one-year Treasury Bill will have a rate of return of 5% over the next year. Also, information from an investment advising service lists the current beta for Tech.com as 1.68 and for Sam’s Grocery as 0.52. You are provided a series of questions to guide your analysis.

Question 1
Using the probabilistic approach, calculate the expected rate of return for Tech.com, Sam’s Grocery and the S&P 500 Index.

Question 2
Calculate the standard deviations in estimated rates of return for Tech.com, Sam’s Grocery and S&P 500.

Question 3
Which is a better measurement of risk for the common stock of Tech.com and Sam’s Grocery—the standard deviation you calculated or the beta?

Question 4
Based on the beta provided, what is the expected rate of return for Tech.com and Sam’s Grocery for the next year?


By: L.D. Young
Corey Oakley
Nate Karlin

Expected Rate of Return
Multiply probability of each outcome by its estimated rate of return and add together
Four outcomes: Recession, Average, Expansion, Boom

Tech.com= .3(-.2)+.2(.15)+.35(.3)+.15(.5)
= 15.07%

Sam’s=.3(.05)+.2(.06)+.35(.08)+.15(.1)
=7%

S&P 500=.3(-.04)+.2(.11)+.35(.17)+.15(.17)
= 11%

Calculate Standard Deviation
Find variance. Subtract rate of return from estimated rate of return for each outcome, then square that number and multiply by its corresponding probability.
Find standard deviation, take square root of the variance.

Solutions
Tech=.3(-.2-.15)2+.2(.15-.15) 2+.35(.3-.15) 2+.15(.5-.15) 2=0.063
Standard deviation= /0.063 = 25.1%

Sam’s=.3(.05-.07) 2+.2(.06-.07) 2+.35(.08-.07) 2+.15(.1-.07) 2 =.00019
Standard deviation=/.00019 = 1.38%

S&P 500=.3(-.04-.11) 2+.2(.11-.11) 2+.35(.17-.11) 2+.15(.27-.11) 2 =0.01185
Standard deviation=/0.01185 = 10.9%

Better measurement of risk:Beta or Standard Deviation?
Beta is better because it measures only the systematic risk, unlike standard deviation, which does not separate systematic risk from unsystematic risk.

Rate of Return for Beta
Tech.com "Beta"= 1.68
 E(Ri) = 0.05+1Use CAPM model  E(Ri) = Rf + B[E(Rm) – Rf]

Risk-free rate is 5% (T-Bill)
Tech.com E(Ri) = .68[0.10-0.05]
0.05+1.68(0.05)
0.05+0.084
=0.134
Expected rate of return for next
year =13.4%

Rate of Return for Beta cont.
Use CAPM model  E(Ri) = Rf + B[E(Rm) – Rf]
Risk-free rate is 5% (T-Bill)
Sam’s Grocery beta = 0.52
Sam’s  E(Ri) = 0.05+0.52[0.10-0.05]
0.05+0.52(0.05)
0.05+0.026
=0.076
Expected rate of return for next
year =7.6%

Question 5
If you form a two-stock portfolio by investing $30,000 in Tech.com and $70,000 in Sam’s Grocery, what is the portfolio beta and expected return?

Portfolio 1
Portfolio Weight
Tech.com Weight
Initial Investment ($30,000) / Portfolio Total (100,000) = .30

Sams Grocery Weight
Initial Investment ($70,000) / Portfolio Total ($100,000) = .70

Portfolio 1 Beta
B(p`1)= .30(1.68) + .70(.52)
.504 + .364
= .868

Portfolio 1 Expected Return
E(r`p)= .30(13.4%) + .70(7.68%)
4.02 + 5.376
= 9.396 or 9.4%

Question 6
If you form a two-stock portfolio by investing $30,000 in Tech.com and $70,000 in Sam’s Grocery, what is the portfolio beta and expected rate of return?

Portfolio 2
Portfolio Weight
Tech.com Weight
Initial Investment ($70,000) / Portfolio Total (100,000) = .70

Sams Grocery Weight
Initial Investment ($30,000) / Portfolio Total ($100,000) = .30

Portfolio 2 Beta
B(p`1)= .70(1.68) + .30(.52)
1.176+.156
= 1.332
Portfolio 2 Expected Return
E(r`p)= .70(13.4%) + .30(7.68%)
9.38 + 2.304
= 11.684 or 11.7%


Question 7
Which of these two-stock portfolios do you prefer?

We would choose Portfolio 2, based on the concept of higher returns

Questions???
Thank You For Your Time & Attention..
Full transcript