Question

1. Following are four economic states, their likelihoods, and the potential returns: Economic State Probability Return Fast growth 0.13 53 % Slow growth 0.64 14 Recession 0.18 –27 Depression 0.05 –60 Compute the expected return and standard deviation. (Do not round intermediate calculations. Round your final answer to 2 decimal places.) Expected return % Standard deviation %

2.

Table 9.2 Average Returns for Bonds

  

		Low-risk bonds
1950 to 1959	Average		2.0	%
1960 to 1969	Average		4.7
1970 to 1979	Average		6.7
1980 to 1989	Average		8.5
1990 to 1999	Average		4.6
2000 to 2009	Average		2.5

Table 9.4 Annual Standard Deviation for T-Bills

	Low-risk bonds
1950 to 1959		1.1	%
1960 to 1969		1.9
1970 to 1979		2.2
1980 to 1989		2.7
1990 to 1999		1.2
2000 to 2009		1.9

   

Use the tables above to calculate the coefficient of variation of the risk-return relationship in T-bills during each decade since 1950. (Round your answers to 2 decimal places.)

   

Decade	CoV
1950s
1960s
1970s
1980s
1990s
2000s

Answer 1

Answer 1.

Fast Growth:
Probability = 0.13
Return = 53%
Slow Growth:
Probability = 0.64
Return = 14%
Recession:
Probability = 0.18
Return = -27%
Depression:
Probability = 0.05
Return = -60%

Expected Return = 0.13 * 53% + 0.64 * 14% + 0.18 * (-27%) + 0.05 * (-60%)
Expected Return = 7.99%

Variance = 0.13 * (0.53 - 0.0799)^2 + 0.64 * (0.14 - 0.0799)^2 + 0.18 * (-0.27 - 0.0799)^2 + 0.05 * (-0.60 - 0.0799)^2
Variance = 0.073799

Standard Deviation = (0.073799)^(1/2)
Standard Deviation = 0.2717
Standard Deviation = 27.17%