YIELD Function

Changes and Enhancements

YIELD Function

calculates yield-to-maturity of a cash-flow stream and returns a scalar

YIELD( times,flows,freq,value)

The YIELD function returns a scalar containing yield-to-maturity of a cash flow stream based on frequency and value specified.

times: is an n-dimensional column vector of times. Elements should be non-negative.
flows: is an n-dimensional column vector of cash flows.
freq: is a scalar that represents the base of the rates to be used for discounting the cash flows. If positive, it represents discrete compounding as the reciprocal of the number of compoundings. If zero, it represents continuous compounding. No negative values are allowed.
value: is a scalar that is the discounted present value of the cash flows.

The present value relationship can be written as

$P=\sum_{k=1}^K c(k) D(t_k)$

where P is the present value of the asset, {c(k)}k = 1,...,K is the sequence of cash flows from the asset, t_k is the time to the k-th cash flow in periods from the present, and D(t) is the discount function for time t.

With continuous compounding:

D(t) = e^{-y t}

With discrete compounding:

D(t) = (1+fy)^-t/f

where f > 0 is the frequency, the reciprocal of the number of compoundings per unit time period, and y is the yield-to-maturity. The YIELD function solves for y.

For example, the following code

   timesn=T(do(1,100,1));
   flows=repeat(10,100);
   freq=50;
   value=682.31027;
   yield=yield(timesn,flows,freq,value);
   print yield;

produces the following output:

   YIELD  
   0.0100001

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