Explain Malkiel\'s theorem with the prices below 6% Coupon Rate Coupon Rate Face

Question

Explain Malkiel's theorem with the prices below 6% Coupon Rate Coupon Rate Face Value $1,000 Time to Maturity 6% Yields 3 Years 6 Years 12 Years 24 Years 27 Years 4.7% 5.3% Price Difference Percentage Change $1,035.98$1,067.29$1,118.20$1,185.89$1,197.69 $1,019.18$1,035.58$1,061.57$1,094.44$1,099.91 $16.80 $31.71 $56.63 $91.45 $97.78 8990 79% 61% 7% 15 Year Bond Coupon Rates Yields 3% 4% 5% 5% 7% 3% 4% 5% 5% $1,000.00$1,120.08$1,240.16$1,360.24$1,480.32 $888.02$1,000.00 $1,111.98$1,223.96$1,335.95 $790.70 $895.35$1,000.00$1,104.65$1,209.30 $705.99 $804.00 $902.00$1,000.00$1,098.00 $632.16 $724.12 $816.08 $908.04$1,000.00

Explanation / Answer

Malkiel’s Theorem states the relationship between bond prices, time to maturity and interest rates.

Theorem 1: Bond prices move inversely with yields

From the table below it can be seen bonds higher yield bonds are (5.3%) priced lower than (4.7%) bonds for all maturities.

Yield

3 years

6 years

12 years

24 years

27 years

4.70%

1035.98

1067.29

1118.2

1185.89

1197.69

5.30%

1019.18

1035.58

1061.57

1094.44

1099.91

Theorem 2: Longer Term Bonds have more Risk

From the table below we can see that as yields rise from 4.7% to 5.3 % price change (both in $ and % terms) is highest for the 27 year maturity bond and lowest for 3 year maturity bond.

Yield

3 years

6 years

12 years

24 years

27 years

4.70%

1035.98

1067.29

1118.2

1185.89

1197.69

5.30%

1019.18

1035.58

1061.57

1094.44

1099.91

$ Difference

-16.8

-31.71

-56.63

-91.45

-97.78

% Difference

-1.62%

-2.97%

-5.06%

-7.71%

-8.16%

Longer term bonds have more duration and hence are more interest rate sensitive.

Theorem 3: Higher Coupon Bonds have less Risk

For the below 15 year bond as yield rise from 3 % to 4% the price change (both in $ and % terms) is lowest for the 7 % coupon bond, while it is highest for bond with the lowest coupon of 3 %.

Coupon

Yield

3%

4%

5%

6%

7%

3%

1000

1120.08

1240.16

1360.24

1480.32

4%

888.02

1000

1111.98

1223.96

1335.95

$ Difference

-111.98

-120.08

-128.18

-136.28

-144.37

% Difference

-11.20%

-10.72%

-10.34%

-10.02%

-9.75%

Similar maturity bonds have higher interest rate sensitivity for lower coupons compared to higher coupons.

Yield

3 years

6 years

12 years

24 years

27 years

4.70%

1035.98

1067.29

1118.2

1185.89

1197.69

5.30%

1019.18

1035.58

1061.57

1094.44

1099.91

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