Please help me with questions regarding stocks and bonds. Thanks for the help! S

Question

Please help me with questions regarding stocks and bonds.

Thanks for the help!

Suppose you gathered the following return data on these types of investments over the previaus three decades: Investment Large-company stocks Small-company stocks Long-term corporate bonds Long-term government bonds U.S. Treasury bills Average Return 14.3% 21.2% 9.7% 7.5% 5.6% Standard Deviation 21.1% 35.3% 10.4% 8.0% 5.2% During this 30-year period, what was the risk premium on large-company stocks? 6.0% O 11.2% o 8.7% O 12.0% o 9.3% If you were to plot the distribution of returns for each of these investments, which investment would have the tightest distribution? In other words, which investment would have the most observations near the average and the narrowest distribution curve? O Short-term govemment bonds O Large-company stocks O Long-term government bonds U.S. Treasury bills O Small-company stocks Which investment exposes the investor to the greatest chance of negative returns in a glven year? O Short-term govermment bonds O Small-company stocks O Large-company stocks U.S. Treasury bills O Long-term government bonds what is the probability of observing a return on large-company stocks that is greater than 35.4%? Assume a normal distribution About 95% About 16% About 32% About 34% About 68%

Explanation / Answer

Part 1:

In this case, US Treasury bills are considered to be the risk free asset. Th return of a risky asset over the risk-free asset is considered to be the Risk premium therefore the risk premium for the large company's stock = return on stock - return on the US treasury bills, which is 14.3-5.6 = 8.7%

Part 2

The one with the lowest standard deviation is the one that will have the tightest distribution therefore going by this logic, US treasury bills having a stadard deviation of 5.2 will have the narrowest distribution.

Part 3:

Up(0.68*0.5=34%): 14.3+21.1=35.4

Down(0.68*0.5=34%): 14.3-21.1=-6.8

Up(0.95*0.5=47.5%): 14.3+2*21.1=56.5

Down(0.95*0.5=47.5%): 14.3-2*21.1=-27.9

Up(0.99*0.5=49.5%): 14.3+3*21.1=77.6

Down(0.99*0.5=49.5%): 14.3-3*21.1=-49

Up(0.68*0.5=34%): 21.2+35.3=56.6

Down(0.68*0.5=34%): 21.2-35.3=-14.1

Up(0.95*0.5=47.5%): 21.2+2*35.3=91.8

Down(0.95*0.5=47.5%): 21.2-2*35.3=-49.4

Up(0.99*0.5=49.5%): 21.2+3*35.3=127.1

Down(0.99*0.5=49.5%): 21.2-3*35.3=-84.7

Up(0.68*0.5=34%): 9.7+10.4=20.1

Down(0.68*0.5=34%): 9.7-10.4=-0.7

Up(0.95*0.5=47.5%): 9.7+2*10.4=30.5

Down(0.95*0.5=47.5%): 9.7-2*35.3=-11.1

Up(0.99*0.5=49.5%): 9.7+3*10.4=40.9

Down(0.99*0.5=49.5%): 9.7-3*10.4=-21.5

Up(0.68*0.5=34%): 7.5+8=15.5

Down(0.68*0.5=34%): 7.5-8=-0.5

Up(0.95*0.5=47.5%): 7.5+2*8=23.5

Down(0.95*0.5=47.5%): 7.5-2*8=-8.5

Up(0.99*0.5=49.5%): 7.5+3*8=31.5

Down(0.99*0.5=49.5%): 7.5-3*8=-16.5

Up(0.68*0.5=34%): 5.6+5.2=10.8

Down(0.68*0.5=34%): 5.6-5.2=0.4

Up(0.95*0.5=47.5%): 5.6+2*5.2=16

Down(0.95*0.5=47.5%): 5.6-2*5.2=-4.8

Up(0.99*0.5=49.5%): 5.6+3*5.2=21.2

Down(0.99*0.5=49.5%): 5.6-3*5.2=-10

Therefore, small stock exposes the investor to the largest negative return.

Part 4:

In case of normal distribution it is believed that movement of 1 standard deviation up or down the mean covers 68% of the area under the curve. In case of a large company stock, the mean is 14.3 and the standard deviation is 21.1 so if the mean goes up by 1 standard deviation, that means the return becomes 14.3+21.1= 35.4, the probability of the retur going up or down is 50% therefore, of the total probability of 68%, half of the times the rate will go up and half of the times it will go down, therefore, 0.5*68=34% of the times the return will reach 35.4%. To exceed this, out of the total 50% of the returns higher that the man return, we reduce the are when the return reaches, 35.4% so the calculation goes like 50-34=16% of times the return will exceed 35.4%

Up(0.95*0.5=47.5%): 9.7+2*10.4=30.5

Down(0.95*0.5=47.5%): 9.7-2*35.3=-11.1

Up(0.99*0.5=49.5%): 9.7+3*10.4=40.9

Down(0.99*0.5=49.5%): 9.7-3*10.4=-21.5

asset average ruturn standard deviation 1 standard deviation (68%) 2 standard deviation (95%) 3 standard deviation (99%) Large stock 14.3 21.1

Up(0.68*0.5=34%): 14.3+21.1=35.4

Down(0.68*0.5=34%): 14.3-21.1=-6.8

Up(0.95*0.5=47.5%): 14.3+2*21.1=56.5

Down(0.95*0.5=47.5%): 14.3-2*21.1=-27.9

Up(0.99*0.5=49.5%): 14.3+3*21.1=77.6

Down(0.99*0.5=49.5%): 14.3-3*21.1=-49

small stock 21.2 35.3

Up(0.68*0.5=34%): 21.2+35.3=56.6

Down(0.68*0.5=34%): 21.2-35.3=-14.1

Up(0.95*0.5=47.5%): 21.2+2*35.3=91.8

Down(0.95*0.5=47.5%): 21.2-2*35.3=-49.4

Up(0.99*0.5=49.5%): 21.2+3*35.3=127.1

Down(0.99*0.5=49.5%): 21.2-3*35.3=-84.7

Long Term Corp 9.7 10.4

Up(0.68*0.5=34%): 9.7+10.4=20.1

Down(0.68*0.5=34%): 9.7-10.4=-0.7

Up(0.95*0.5=47.5%): 9.7+2*10.4=30.5

Down(0.95*0.5=47.5%): 9.7-2*35.3=-11.1

Up(0.99*0.5=49.5%): 9.7+3*10.4=40.9

Down(0.99*0.5=49.5%): 9.7-3*10.4=-21.5

Long term Govt. bonds 7.5 8.0

Up(0.68*0.5=34%): 7.5+8=15.5

Down(0.68*0.5=34%): 7.5-8=-0.5

Up(0.95*0.5=47.5%): 7.5+2*8=23.5

Down(0.95*0.5=47.5%): 7.5-2*8=-8.5

Up(0.99*0.5=49.5%): 7.5+3*8=31.5

Down(0.99*0.5=49.5%): 7.5-3*8=-16.5

US Treasury bill 5.6 5.2

Up(0.68*0.5=34%): 5.6+5.2=10.8

Down(0.68*0.5=34%): 5.6-5.2=0.4

Up(0.95*0.5=47.5%): 5.6+2*5.2=16

Down(0.95*0.5=47.5%): 5.6-2*5.2=-4.8

Up(0.99*0.5=49.5%): 5.6+3*5.2=21.2

Down(0.99*0.5=49.5%): 5.6-3*5.2=-10

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