Question

6. Here is a list of five individual FICO credit scores. What is their average and standard deviation?

• 671
• 745
• 810
• 778
• 801

8. Widget Inc. Stock has the following probabilities of return. What is its mu and sigma?

• There is a 30% chance for a good economic outlook and the stock will increase by 25%
• There is a 40% chance for an okay economic outlook and the stock will increase by 5%
• There is a 30% chance for a bad economic outlook and the stocks will decline by -25%

9. The following data was obtained on two individual stocks. What is their correlation? What does the number mean?

	Stock A	Stock B
Year 1 return	12%	8%
Year 2 return	7%	16%
Year 3 return	10%	12%

10. You are purchasing a factory for $120,000 at a nominal rate of 10% and the terms of the agreement are for 20 equal payments to retire the debt. What is the yearly payment

Answer 1

Answer 1:

FICO Credit

Let the score be X, average is represented by X'

	X	(X-X')2
1	671	9205156
2	645	9363600
3	810	8381025
4	778	8567329
5	801	8433216
Total	3705	43950326
Total/5	741	54869
	X'	Variance

Average = 741

Standard Deviation (SD) = (Variance)^0.5 = 234

Asnwer 2:

mu: average

sigma: Standard Deviation (SD)

Let the return on stock of wIdget inc be X and probability of the same be P

	P	X	P(X)	P(X-X')2
1	0.3	671	201	294
2	0.4	645	258	1,313
3	0.3	810	243	3,480
Total			702	5,087
			X'	Variance

Average = 702

Standard Deviation (SD) = (Variance)^0.5 = 71.32

Answer 3

Let return on sock A be X and Return on stock B be Y

	X	Y	(X-X')2	(Y-Y')2	(X-X')(Y-Y')
1	12	8	5	16	-9.33
2	7	16	7	16	-10.67
3	10	12	0	-	0.00
Total	29	36	13	32	-20
Total/3	9.67	12.00	4.22	10.67	-6.67
	X'	Y'	Variance of X	Variance of Y	Co Variance of X and Y

Standard Deviation (SD) of A = (Variance of A)^0.5 = 2.05 %

Standard Deviation (SD) of B = (Variance of B)^0.5 = 3.27 %

Co variance between A & B = -6.67 %

Co variance = SD_A*SD_B*correlation(r)

-6.67 = 2.05*3.27* r

Correlation (r) = -0.99

The relation between the two stocks is negative, that means if a stock will rise then other will decliene by a factor of 0.99.

Answer 4

Let the amount be A

This implies

120000 = A* (Present Value Annuity Factor (10%,20)

120000 = A* 8.51

A = $ 14101