Question

1. (14 pts) The Grunewald Company has developed the following data regarding the rates of return on a potential stock and the market:

State of the Economy of Each                                                Rates of Return If State occurs

	State Occuring
Deep Recession	.20
Mild Recession	.20
Average	.20
Mild boom	.20
Strong boom	.20

Stock A	Market
(20%)	(30%)
10	5
15	20
20	25
25	30

                                                    

1. Caculate the standard deviations for the stock A and the Market.
2. Calculate the betas for the stock A and the market
3. Calculate the probability that stock A’s return is negative, that is P (K<0)=?
4. Calculate the probability that stock A’s return is between 0 and 15%, that is P (0<K<15)=?
5. Calculate the Covariance and correlation coefficient between stock A and the market.

PLEASE: If possible, do step by step with the Financial calculator HP10BII

Answer 1

a) Standard Deviation = Square Root of [Sum of all (Probability x [Return - Mean of Return]²])

• Standard Deviation of Stock: 15.81% [i.e., Square root of variance of 2.5%]; values from table below]
• Standard Deviation of Market: 26.65% [i.e., Square root of variance of 7.1%; values from table below]

• 	Probability	Return of Stock	Stock's Probability x (Return - Mean)2	Return of Market	Market's Probability x (Return - Mean)2	Probability x (Stock Return - Mean of Stock Return) x (Market Return - Mean of Market Return)
  	0.2	-20.00%	1.80%	-30%	3.20%	2.40%
  	0.2	10.00%	0.00%	5%	0.05%	0.00%
  	0.2	15.00%	0.05%	20%	0.80%	0.10%
  	0.2	20.00%	0.20%	25%	1.25%	0.30%
  	0.2	25.00%	0.45%	30%	1.80%	0.60%
  Total		50.00%	2.50%	50.00%	7.10%	3.40%
  Mean: Total/5		10.00%		10.00%

b) Betas: Covariance of Stock with Market / Variance of Market

• Beta of Stock: 0.48 [3.40% / 7.10% = 0.4788 (can be rounded to 0.48); these values are in the table above]
• Beta of Market: 1 [Beta of market is always 1]

c) Probability that stock's return is negative: 20% = 0.20

d) Probability that stock's return is between 0% and 15%: 40% = 0.40 [being 20% + 20%]

e) Covariance between stock and the market: 3.40% [in the table above]
Correlation between stock and market: 0.8070 [being [Covariance / SD of Stock x SD of Market] = 3.40% / (15.81% x 26.65%)]

Hope this helps. I used normal calculator. It must be easier in Financial calculator - but I do not have that model.
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