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Relationship between yield and term to maturity on securities that differ only in length of time to maturity
A yield curve is a graphical representation of the term structure; it shows the relationship between maturity and a security's yield at a point in time.
The yield curve may be ascending (normal), flat, or descending (inverted).
Several theories explain the shape of the yield curve.
The shape of the yield curve is determined solely by expectations of future interest rate movements, and changes in these expectations lead to changes in the shape of the yield curve .
Ascending: future interest rates are expected to increase.Descending: future interest rates are expected to decrease.
Long-term interest rates are geometric averages of current and expected future (implied, forward) interest rates.
Maturity preferences by investors may affect security prices (yields), explaining variations in yields by time
Market participants have strong preferences for securities of particular maturity and buy and sell securities consistent with their maturity preferences.
If market participants do not trade outside their maturity preferences, then discontinuities and spikes are possible in the yield curve.
The Preferred Habitat Theory (PH) is an extension of the Market Segmentation Theory.
PH allows market participants to trade outside of their preferred maturity if adequately compensated for the additional risk.
PH allows for humps or twists in the yield curve, but limits the discontinuities possible under Segmentation Theory. PH is consistent with a smooth yield curve.
Day-to-day changes in the term structure are most consistent with the Preferred Habitat Theory.
However, in the long-run, expectations of future interest rates and liquidity premiums are important components of the position and shape of the yield curve.
Investors charge a default risk premium (above riskless or less risky securities) for added risk assumed
DRP = i - irf
The default risk premium (DRP) is the difference between the promised or nominal rate and the yield on a comparable (same term) riskless security (Treasury security).Investors are satisfied if the default risk premium is equal to the expected default loss.
The taxation of security gains and income affects the yield differences among securities
The after-tax return, iat, is found by multiplying the pre-tax return by one minus the investor’s marginal tax rate: iat = ibt(1-t)Municipal bonds’ interest income is tax exempt.
Various option provisions may explain yield differences between securitiesAn option is a contract provision which gives the holder or the issuer the right, but not the obligation, to buy, sell, redeem, or convert an asset at some specified price within a defined future time period.
A put option permits the investor (lender) to sell the bond back to the issuer at a prespecified price before maturityInvestors are likely to put their bonds during periods of increasing interest rates. The difference in interest rates between putable and nonputable contracts is called the put interest discount (PID).
PID = ip - inp
The yield on a putable bond, ip, will be lower than the yield on the nonputable bond, inp, by the PIP.
A conversion option permits the investor to convert a bond into another security (usually common stock)Convertible bonds generally have lower yields, icon, than nonconvertibles, incon.The conversion yield discount (CYD) is the difference between the yields on convertibles relative to nonconvertibles.
CYD = icon - incon. Investors accept lower yields on convertibles because they have an opportunity for increased rates of return through conversion.