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3 years ago

7

The stock of Business Adventures sells for $50 a share. Its likely dividend payout and end-of-year price depend on the state of

the economy by the end of the year as follows: Dividend Stock Price Boom $3.00 $60 Normal economy 1.20 58 Recession 0.75 49 a. Calculate the expected holding-period return and standard deviation of the holding-period return. All three scenarios are equally likely. (Do not round intermediate calculations. Round your answers to 2 decimal places.)

1 answer:

Delvig [45]3 years ago

7 0

Answer:

Holding period return = 14.49%, Standard Deviation = 11.08 approx

Explanation:

Eco Scenario Dividend Stock Price HPR Prob Expected HPR

Boom 3 60 26 0.33 8.58

Normal 1.2 58 18.4 0.33 6.072

Recession 0.75 49 (0.5) 0.33 <u> (0.165)</u>

Expected HPR 14.49%

<u>Calculation Of Standard Deviation</u>

(A) (B) (A) - (B)

$P_{1}$ $P_{0}$ $D_{1}$ Given return Exp return d p $p.d^{2}$

60 50 3 26 14.49 11.51 0.33 43.718

58 50 1.2 18.4 14.49 3.91 0.33 5.045

49 50 0.75 (0.5) 14.49 14.99 0.33 <u> 74.15</u>

Total $p.d^{2}$ = 122.91

wherein, d = deviation

p = probability

Standard Deviation = $\sqrt{Total\ p.d^{2} }$ = $\sqrt{122.91}$ = 11.08

<u></u>

<u>Working Note</u>:

Holding period return = $\frac{P_{1}\ -\ P_{0} \ +\ D_{1} }{P_{0} }$

Boom = $\frac{60\ -\ 50 \ +\ 3 }{50 }$ = 26%

Similarly, for normal = $\frac{58\ -\ 50 \ +\ 1.2 }{50 }$ = 18.4%

Recession = $\frac{49\ -\ 50 \ +\ 0.75 }{50}$ = (0.5)%

figure in bracket indicates negative return

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