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Yield
Source: Encyclopedia of Banking & Finance (9h Edition) by Charles J Woelfel
(We recommend this as work of authority.)

Investment income; investment rate of return, as distinguished from a speculative or temporary rate of return; the net income from property, but particularly applied to bonds bought as investments to be held to maturity.

The yield of a bond depends upon four variables:  (1) price, (2) INTEREST rate, (3) interest period, and (4) term, i.e., remaining life of the bond to maturity.  The third variable may be omitted for practical purposes, since the interest on most bonds is payable semi-annually.  Bonds paying interest annually are less valuable than like bonds paying interest semi-annually, but this difference for all practical purposes is negligible

A 5% bond purchased at par, regardless of its term, yields 5%.  But if it is purchased at a premium, its yield to maturity is less, and if it is purchased at a discount, its yield is more, depending upon the term, because of amortization of the premium in the former case and accretion of the discount in the latter case, both on a per annum basis.  The exact yield to maturity of a bond bought at a premium or discount is mathematically the internal rate of return - the discount rate which applies in equating the sum of the present values of interest payments and the principal with the present market price.  This is the mathematical basis for the bond yields and values tables which are customarily referred to for convenience.  (See BOND VALUES TABLE.)  A 4% bond (interest payable semi-annually) having 20 years to run and purchased at a premium of \$35, i.e., \$1,035, yields 3.75%, but if purchased at a discount of \$33.50, i.e., \$966.50, it yields 4.25%.

Bid and asked quotations on treasury notes and bills and state and municipal issues, bankers acceptances, and commercial paper are quoted on a yield basis.  Prices are quoted "at a price to yield percent" since, when other factors are equal, yield is the only common denominator for comparison of market prices and investment values.

Yield / Return

The terms yield and RETURN are often confused.  The first is restricted in its meaning to the net income from a bond if held to maturity, whereas return denotes current income derived from either a bond or stock, without reference to maturity.  In the case of stock, the variables mentioned above are not fully known.  There is no term or maturity value, nor is the income certain; therefore yield cannot be computed, except by assuming a given holding period so that holding period yield (HPY) can be computed.  The current return of a bond or stock is determined by dividing the purchase price into the annual cash interest or dividend.  In the above case, where the purchase price of the bond is \$1,035 and the cash interest \$40, the current return is 3,865%, whereas the yield to maturity is 3.75%.  The current return of a bond bought at a premium is higher than its yield, since no deduction need be made for amortization of the premium, which is lost when the bond matures.  Conversely, the current return on a bond bought at a discount is lower than its yield to maturity, since the investment value of the bond increases as it approaches maturity as the result of accretion of the discount.

The yield on optional bonds selling at a premium should be computed on the shortest possible time they may be outstanding.  If the optional bonds are selling at a discount, the yield should be computed upon the longest possible time they may be outstanding.

## BIBLIOGRAPHY

FINANCIAL PUBLISHING Co. Comprehensive Bond Values Table.
WOELFEL, F.J. Money, Time, Interest, and Yields, 1988.

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