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In finance, the weighted-average life (WAL) of an amortizing loan or amortizing bond, also called average life, [1] [2] [3] is the weighted average of the times of the principal repayments: it's the average time until a dollar of principal is repaid. In a formula, [4] = =,
The number weighted average of the times of the principal repayments of an amortizing loan is referred to as the weighted-average life (WAL), also called "average life". It's the average time until a dollar of principal is repaid. In a formula, = =, where:
The weighted mean in this case is: ¯ = ¯ (=), (where the order of the matrix–vector product is not commutative), in terms of the covariance of the weighted mean: ¯ = (=), For example, consider the weighted mean of the point [1 0] with high variance in the second component and [0 1] with high variance in the first component.
Similarities in both values and definitions of Macaulay duration versus Weighted Average Life can lead to confusing the purpose and calculation of the two. [12] For example, a 5-year fixed-rate interest-only bond would have a Weighted Average Life of 5, and a Macaulay duration that should be very close. Mortgages behave similarly.
Exponential smoothing or exponential moving average (EMA) is a rule of thumb technique for smoothing time series data using the exponential window function. Whereas in the simple moving average the past observations are weighted equally, exponential functions are used to assign exponentially decreasing weights over time. It is an easily learned ...
The rate of return on a portfolio can be calculated indirectly as the weighted average rate of return on the various assets within the portfolio. [3] The weights are proportional to the value of the assets within the portfolio, to take into account what portion of the portfolio each individual return represents in calculating the contribution of that asset to the return on the portfolio.
The Marshall-Edgeworth index, credited to Marshall (1887) and Edgeworth (1925), [11] is a weighted relative of current period to base period sets of prices. This index uses the arithmetic average of the current and based period quantities for weighting. It is considered a pseudo-superlative formula and is symmetric. [12]
Average life may refer to: Average life span, statistical life expectancy for a certain population; Exponential decay#Mean lifetime, average survival time in an exponentially decreasing set; Weighted-average life, loan repayment timing