Question

Consider the following rates of return: Year Large-Company Stocks US Treasury Bills 1 3.99 % 4.59 % 2 14.16 4.94 3 19.25 3.86 4 –14.43 6.99 5 –31.92 5.30 6 37.49 6.20 a. Calculate the arithmetic average returns for large-company stocks and T-bills over this period b. Calculate the standard deviation of the returns for large-company stocks and T-bills over this period. c. Calculate the observed risk premium in each year for the large-company stocks versus the T-bills. What was the arithmetic average risk premium over this period? D.Calculate the observed risk premium in each year for the large-company stocks versus the T-bills. What was the standard deviation of the risk premium over this period?

12.50 points Consider the following rates of return; Large- Year Company Stocks 3.99 % 14.16 19.25 -14.43 -31.92 37.49 US Treasury Bills 4.59 % 4.94 3.86 6.99 on a. Calculate the arithmetic average returns for large-company stocks and T-bi round intermediate calculations and enter your answers as a perce places, e.g.. 32.16.) Large-company stocks Average returns T-bills b. Calculate the standard deviation of the returns for large company stocks and Do not found intermediate calculations and enter your answers as a p decimal places, e.g-, 32.16.) Large-company stocks Standard deviation Tbili 1. Calculate the observed risk premium in each year for the large-company stocks What was the arithmetic average risk premium over this period? A negative an indicated by a minus syn. Do not found internediate calculations and enterye percent rounded to 2 decimal places... 32.16.) Average tek pem O type here to search

Answer 1

Basic calculations

Let .......... X = Returns of large company stocks

................Y = Returns of T-Bills

Year	X	Y	Dx	Dy	Dx2	Dy2
1	3.99	4.59	-0.76667	-0.72333	0.587783	0.523211
2	14.16	4.94	9.40333	-0.37333	88.42262	0.139378
3	19.25	3.86	14.49333	-1.45333	210.0566	2.112177
4	-14.43	6.99	-19.1867	1.676667	368.1283	2.811212
5	-31.92	5.3	-36.6767	-0.01333	1345.178	0.000178
6	37.49	6.2	32.73333	0.886667	1071.471	0.786178
Total	28.54	31.88		Variance	3083.844	6.372333
Average	4.76	5.31		SD	55.53	2.52

Question - (a)

Arithmetic average = Sum of the values / number of values

Large Company stocks = 28.54 / 6 = 4.75667 .............. = 4.76 %

T - Bills = 31.88 / 6 = 5.31333.........................................= 5.31 %

Question - (b)

For computing the standard deviations ......... we need Dx and Dy

Dx = X - Average of X ......... Note that, to reduce the error of intermediate rounding, we subtract 4.75667 instead of 4.76.

Dy = Y - 5.31333

Large company stock ............Variance = Σ Dx² = 3038.84 and Standard deviation = √3038.84 = 55.53 %

T-Bill ......................................Variance = Σ Dy² = 6.372333 and Standard deviation = √6.372333 = 2.52 %

Question - (c)

Observed Risk premium = X - Y

Z = X - Y

Year	Z	Dz	Dz2
1	-0.6	-0.04333	0.001877
2	9.22	9.77667	95.58328
3	15.39	15.94667	254.2963
4	-21.42	-20.8633	435.2785
5	-37.22	-36.6633	1344.2
6	31.29	31.84667	1014.21
Total	-3.34	Variance	3143.57
Average	-0.56	SD	56.07

Arithmetic average of risk premium = - 0.56

Standard deviation = 56.07