Wall Street Journal Reports The Rate On 6

Here It Isthe Wall Street Journalreports That The Rate On 6 Year Treas

The Wall Street Journal reports that the rate on 6-year Treasury securities is 1.95 percent and the rate on 8-year Treasury securities is 2.90 percent. According to the unbiased expectations hypothesis, what does the market expect the 2-year Treasury rate to be six years from today, E (6 r 2)? (Do not round intermediate calculations and round your answer to 2 decimal places.)

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The unbiased expectations hypothesis (UEH) is an important theory in finance that suggests that the yield on long-term bonds is equal to the average of current and expected future short-term interest rates. This hypothesis assumes that investors are indifferent between holding long-term bonds and rolling over short-term bonds, and thus, the forward rates embedded in long-term bond yields can be interpreted as market expectations of future short-term interest rates. This principle allows us to predict future interest rates from current yield data, making it a valuable tool for understanding the expectations embedded in bond markets.

In this scenario, we have the current yields for 6-year and 8-year Treasury securities. Specifically, the 6-year Treasury yield (Y6) is 1.95%, and the 8-year Treasury yield (Y8) is 2.90%. The goal is to determine the market's expectation of the 2-year interest rate starting six years from now, denoted as E(6 r2). This involves using the unbiased expectations hypothesis to relate these yields to the expected future short-term rate.

Mathematically, the yield on an n-year bond can be represented as the average of the current and expected future short-term interest rates over the same period. The formula for the yields in terms of expectations is:

Yn ≈ (1/n) × [r0 + E(r1) + ... + E(rn-1)]

where Yn is the yield on the n-year bond, and E(rk) is the expected short-term rate k years from now.

Using the expectations hypothesis, we can express the 8-year yield as the average of the 6-year yield and the expected 2-year rate starting in 6 years. That is:

Y8 ≈ (6/8) Y6 + (2/8) E(6 r2)

Rearranging this formula to solve for E(6 r2), we get:

E(6 r2) = 4 × [Y8 - (6/8) × Y6]

Substituting the known values:

E(6 r2) = 4 × [2.90% - (6/8) × 1.95%]

E(6 r2) = 4 × [2.90% - 1.4625%]

E(6 r2) = 4 × 1.4375%

E(6 r2) = 5.75%

Therefore, the market expects the 2-year Treasury rate to be approximately 5.75% six years from now.

This calculation demonstrates how the unbiased expectations hypothesis allows us to interpret current long-term yields as an aggregation of present and future short-term rate expectations. The significant difference between the current yields and the expected future short-term rate emphasizes market expectations of rising interest rates over this period, possibly reflecting anticipated economic growth or inflationary pressures.

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