The pure expectations theory, or the expectations hypothesis, asserts that long-
ID: 2811660 • Letter: T
Question
The pure expectations theory, or the expectations hypothesis, asserts that long-term interest rates can be used to estimate future short-term interest rates. Based on the pure expectations theory, is the following statement true or false? The pure expectations theory assumes that investors do not consider long-term bonds to be riskier than short-term bonds rue O False The yield on a one-year Treasury security is 4.6900%, and the two-year Treasury security has a 5.6300% yield Assuming that the pure expectations theory is correct, what is the market's estimate of the one-year Treasury rate one year from now? 7.5012% 6.5800% O 8.356690 O 5.593090 Recall that on a one-year Treasury security the yield is 4.6900% and 5.6300% on a two-year Treasury security Suppose the one-year security does not have a maturity risk premium, but the two-year security does and it is 0.1500%. what is the market's estimate of the one-year Treasury rate one year from now? 7.9760% O 6.2800% 5.338090 O 7.1590% Suppose the yield on a two-year Treasury security is 5.83%, and the yield on a five-year Treasury security is 6.20% Assuming that the pure expectations theory is correct, what is the market's estimate of the three-year Treasury rate two years from now? O 7.10% 6.45% 6.53% 6.69%Explanation / Answer
Part 1 The Statement is True. According to the pure expectations theory, Bond yields are only the weighted average of current and expected interest rates and maturity premium don't play a part in yield calculation.
Part 2 According to expectations theory, holding the 2 year bond and holding the 1 year bond and then another 1 year bond at the end of first year would yield the same results. By this logic we can conclude the following:
(1+0.0563)^2 = (1+0.0469)(1+X)
(1+X) = [(1.0563)^2]/1.0469) = 1.06578
So the 1 year treasury yield 1 year from now would be 1.06578 - 1 = 6.58%
Part 3 In this problem, we will operate in a similar manner except that we will subtract the maturity premium from the 2 year yield. So we take the 2 year yield to be: 5.63% - 0.15% = 5.48%.
Repeating the same steps above, we will get:
(1.0469)(1+X) = (1.0548)^2
1+X = 1.062759
X = 6.28%
Part 4 This would work in the same manner as Part 2 except for the powers. The expecation looks something like this:
(1.0583)^2 * (1+X)^3 = (1.062)^5
(1+X)^3 = 1.2062
1+X = 1.06447
X = 6.45%
Hope that helps! :)
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