Expectations hypothesis

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the expectation hypothesis of the term structure of interest rates (whose graphical representation is known as the yield curve) is the proposition that long-term interest rates are determined purely by current and expected short-term rates, such that the final value the expected wealth of investments in short-term bond sequences equals the final value of wealth from investments in long-term bonds.

This hypothesis assumes that various maturities are a perfect substitute and show that the shape of the yield curve depends on the expectations of the market participants about future interest rates. This expected rate, together with the assumption that arbitrage opportunities will be minimal, is sufficient information to build a complete yield curve. For example, if the investor has expectations about what the 1-year interest rate will be next year, the 2-year interest rate can be calculated as a merger of interest rates this year with interest rates next year. More generally, returns (1 result) on a long-term instrument equals the geometric average of returns on a set of short-term instruments, such as those granted by

$Â\; Â{\displaystyle Â\; Â\; Â\; Â\; Â\; Â\; Â(Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â1Â\; Â\; Â\; Â\; Â\; Â\; Â\; ÂÂ\; Â\; Â\; Â\; Â\; Â\; Â}$ _{            me                Â <     ÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂï <½                                   )                 Â ·                           =        (         1                            me                ÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂﯯ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ï <½ï <½ï <½ï <½ï <½ï <½ï <½ï <     ÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂï <½                                 year 1                         )        (         1                            me                ÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂﯯ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ï <½ï <½ï <½ï <½ï <½ï <½ï <½ï <     ÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂï <½                                 year 2                         )         ?        (         1                            me                ÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂﯯ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ï <½ï <½ï <½ï <½ï <½ï <½ï <½ï <     ÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂï <½                                  year n                         )         ,           < {\ displaystyle (1 i_ {lt}) ^ {n} = (1 i_ {st} ^ {\ text {year 1}}) (1 i_ {st} ^ {\ text {year 2}}) \ cdots (1 i_ {st} ^ {\ text {year n}}),}  Â}

where lt and st each refers to long-term and short-term bonds, and where the interest rate i for years to come is value which are expected. This theory is consistent with the observation that results usually move together. However, he failed to explain persistence in the form of non-horizontal yield curves.

Video Expectations hypothesis

Definitions

The expectation hypothesis states that the current price of an asset is equal to the amount of future dividends being discounted which is expected to depend on the information now known. Mathematically if there is a discrete dividend payment $Â\; Â{\displaystyle Â\; Â\; Â\; Â\; Â\; Â\; Â}$ _{    Â     d                ÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂï <½                                {\ displaystyle d_ {t}}} at ${\ displaystyle t = 1,2,...}$ and with a risk-free level ${\ displaystyle r}$ then the price at ${\ displaystyle t}$ is provided by

$Â\; Â{\displaystyle Â\; Â\; Â\; Â\; Â\; Â\; Â}$ _{    Â   P                ÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂï <½                          =                   ?                 Â ·             =     ÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂï <½     Â    Â 1                                 ?                                            Â (                ÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂ...     Â 1
      Â 1                                 r        ÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂ,        ÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂ,                       Â )                           Â ·      ÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÃ, -     ÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂï <½                                     E                [            Â     d                 Â ·                           |                                            F                                      ÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂï <½                         ]               {\ displaystyle P_ {t} = \ number _ {n = t 1} ^ {\ infty} \ left ({\ frac {1} {1 r }} \ right) ^ {nt} \ mathbb {E} [d_ {n} \ mid {\ mathcal {F}} _ {t}]}  Â}

di mana ${\ displaystyle {\ mathcal {F}} _ {t}}  ÂÂ$ adalah penyaringan yang mendefinisikan pasar pada saat ${\ displaystyle t}  ÂÂ$ .

Khususnya, harga obligasi kupon, dengan kupon yang diberikan oleh ${\ displaystyle m_ {t}}  ÂÂ$ pada waktu ${\ displaystyle t}  ÂÂ$ , diberikan oleh

${\ displaystyle P_ {t} = \ jumlah _ {n = t 1} ^ {\ infty} m_ {n} B (t, n) = {\ frac { m_ {t 1}} {1 r (t, t 1)}} {\ frac {1} {1 r (t, t 1)}} \ mathbb {E} [P_ {t 1} \ pertengahan {\ mathcal {F}} _ {t}]}  ÂÂ$

The expectations hypothesis ignores the inherent risks in investing in bonds (since the forward rates are not a perfect predictor of future interest rates). In particular this can be divided into two categories:

1. Interest rate risk
2. Risk of investment returns

It has been found that the expectation hypothesis has been tested and rejected using various interest rates, over various time periods and monetary policy regimes. This analysis is supported in a study conducted by Sarno, where it was concluded that while conventional bivariate procedures provide mixed results, stronger testing procedures, such as expanded vector autoregression tests, suggest rejection of expectation hypotheses across the spectrum of maturity examined. The general reason given for the failure of the expectation hypothesis is that the risk premium is not constant as expected by the expectation hypothesis, but varies in time. However, research by Guidolin and Thornton (2008) suggests otherwise. It is postulated that the expectation hypothesis fails because short-term interest rates can not be predicted to a significant degree.

While traditional term-structure tests largely indicate that the expected future interest rate is an inefficient estimate, Froot (1989) has an alternative to take it. At a short maturity, the expectation hypothesis fails. However, at long maturity, changes in the yield curve reflect changes in expected future levels for one-for-one.

Maps Expectations hypothesis

References

Source of the article : Wikipedia