Question

As CFO of Wolverine World Wide, your personal investments are not very diversified. Approximately 80% of your net worth is in WWW common stock.

Wolverine World Wide (Beta: 1.58, Sigma: 22.63%, Expected Return: 13.47%)

1. What is your 95% confidence interval for next year’s returns in WWW common stock? (4pts)

2. If the 7 year Treasury bill has an expected return of 2.5%, and the S&P 500 returns 8.7% next year, how do you expect Wolverine World Wide to perform based on its Beta? (4pts)

Starbucks: SBUX (Beta: 0.70, Sigma: 13.85%, Expected Return: 11.47%, Correlation to WWW: -0.15)

3. You decide to invest 20% of your investible assets into Starbucks: SBUX. Calculate the new portfolio risk. (8pts)

4. What is the new portfolio expected return? (3pts)

5. What is the new 95% confidence interval for the portfolio? (3pts)

Answer 1

Solution:

1)

95% confidence interval is given by : Mean Value +- z*(sigma/sqrt(n))

n = 1 , Z(95%) = 1.96, sigma = .2263 , mean value (expected return) = .1347

Putting the values in the formula we get:

CO = .1347 +- 1.96(.2263/ sqrt(1)) = .1347 +- 1.96*.2263 = .1347 +- .4435 = .5782 and -.3088

So the Next year's return would be in the range:

-.3088 < Next Year return < .5782

2) Beta of a Tbill is zero while the beta of WWW is 1.58 i.e. it is greater than the beta of the market of 1.

It will be move 1.58 times both on the upside as well as downside as compared to the market.

Expected Return as per CAPM = Rf + beta( Rm - Rf)

Rf -> Risk free rate = 2.5% , Rm-> Market return = 8.7%

E(R) = .025 + 1.58 * (.087 - .025) = .025 + 1.58*.062 = .025 + .097 = .12296

Next year return would be .12296 or 12.29%

3)

Portfolio risk = Sqrt (Sigma1 ^ 2 * w1^2 + Sigma2 ^ 2 * w2^2 + 2 * w1 * w2 * sigma1 * sigma2 ^ Corr(security1 and sec 2)

We have with us

W1 weight of www) = .80 , W2 (weight of SBUX) = .20 , sigma1 (std dev of www) = .2263 , sigma2 (std dev of sbux) = .1385

Corr (www & sbux) = -0.15

Putting all the values in the formula we get:

Portfolio risk = sqrt { (.2263)^2 * (.80)^2 + (.1385)^2 * (.20)^2 + 2 * (.80) * (.20) * (.2263) * (.1385) * (-0.15) }

= sqrt{ (.05121) * (.64) + (.0191)* (.04) + (- .001504) }

= sqrt{ .03277 + .000767 - .001504 }

= sqrt (.03203) = .17899

Portfolio risk = 17.89%

4) Portfolio Expected return = W1 * Return 1 + W2 * Return 2

W1 -> Weight of www = .80 , Return1 -> return of www = .1347 (given)

W2-> Weight of SBUX = .20 return2 -> return of SBUX = .1147 (given)

PER = .80 * .1347 + .20 * .1147 = .10776 + .02294 = .1307 = 13.07%

The portfolio expected return = 13.07%

5) Portfolio CI => Return +- 1.96 * (sigma /sqrt(1))

= .1307 +- 1.96 * (.1789) {calculated in previous parts}

= .1307 +- .3506 = .4813 and -.2199

The portfolio ER lies between -21.99 % to 48.13%