YIELD Function

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YIELD Function

calculates yield-to-maturity of a cash flow stream

YIELD( times, flows, freq, value)

The inputs to the YIELD function are as follows:

times: is an n-dimensional column vector of times.
flows: is an n-dimensional column vector of cash flows.
freq: is a scalar which 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 which is the discounted present value of the cash flows.

The YIELD function returns a scalar which is the yield-to-maturity of a cash flow stream. 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 cashflow 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 compunding,

D(t) = (1+y)^[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.

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