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Bond Fund Rate of Return Scenario Severe recession Mild recession Normal growth Boom Stock Fund Rate of Return -415 -11.09 Pr
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Answer #1

a.

Mean return

13.5 %

Variance

4.6675 %

Explanation:

Stock Fund

Scenario

Probability (a)

Rate of return (b)

(c) =

(a) x (b)

Deviation from expected return (d) = (b) - E(R)

Squared deviation

(e) = d2

(f) = (a) x (e)

Severe recession

0.05

-0.41

-0.0205

-0.5445

0.29648025

0.014824013

Mild recession

0.20

-0.11

-0.0220

-0.2445

0.05978025

0.01195605

Normal growth

0.30

0.08

0.0240

-0.0545

0.00297025

0.000891075

Boom

0.45

0.34

0.1530

0.2055

0.04223025

0.019003613

Expected return E(R)

0.1345

Variance

0.04667475

Expected return or Mean return = 0.1345 or 13.5 %

Variance = 0.04667475 or 4.6675 %

b.

Co-variance

0.6823%

Explanation:

Scenario

Probability (a)

Stock Fund Rate of Return

Bond Fund Rate of Return

Si

Si- Sm

Bi

Bi- Bm

(Si-Sm) x

(Bi-Bm)

Severe recession

0.05

-0.41

-0.18

-0.0205

-0.155

-0.009

-0.07

0.01085

Mild recession

0.20

-0.11

0.14

-0.022

-0.1565

0.028

-0.033

0.0051645

Normal growth

0.30

0.08

0.05

0.024

-0.1105

0.015

-0.046

0.005083

Boom

0.45

0.34

0.06

0.153

0.0185

0.027

-0.034

-0.000629

Mean Sm

0.1345

Mean Bm

0.061

0.0204685

0.006822833

Covariance = ∑ (Si-Sm) x (Bi-Bm)/ (n -1)

                     = (0.01085 + 0.0051645 + 0.005083 - 0.000629)/ (4 -1)

                     = 0.0204685/3 = 0.006822833 or 0.6823 %

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