tmval.Payments.dw_approx

tmval.value.Payments.dw_approx(self, a: float = None, b: float = None, w_t: float = None, k_approx: bool = False, k: float = 0.5, annual: bool = False) → tmval.rate.Rate

Calculates the approximate dollar-weighted yield rate by standardizing the investment time to 1:

j \approx \frac{I}{A + \sum_{t \in (0, 1)} C_t(1-t)}

Where A is the beginning balance, I is interest earned, and the Cs are the contributions. When k_approx is set to true, k is assumed to be a fixed constant within the investment window:

j \approx \frac{I}{A + C(1-k)}

The default value for k is 1/2, simplifying the above expression to:

j approx frac{2I}{A + B - I}

Where B is the withdrawal balance. When arguments a, b, and w_t (corresponding to A, B, and the the withdrawal time) are not provided, a is assumed to be the first payment in the parent object, and b is calculated to be the last.

Parameters

  • a (float) – The initial balance.

  • b (float) – The withdrawal balance.

  • w_t (float) – The withdrawal time.

  • k_approx (bool) – Whether you want to use the k-approximation formula.

  • k (float) – The value for k in the k-approximation formula, defaults to .5.

  • annual (bool) – Whether you want the results annualized.

Returns

The approximate dollar-weighted yield rate.

Return type

Rate