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The actuarial present value (APV) is the expected value of the present value of a contingent cash flow stream (i.e. a series of payments which may or may not be made). Actuarial present values are typically calculated for the benefit-payment or series of payments associated with life insurance and life annuities .
As an example, consider a whole life insurance policy of one dollar issued on (x) with yearly premiums paid at the start of the year and death benefit paid at the end of the year. In actuarial notation, a benefit reserve is denoted as V. Our objective is to find the value of the net level premium reserve at time t.
The first term in the RHS describes short-run impact of change in on , the second term explains long-run gravitation towards the equilibrium relationship between the variables, and the third term reflects random shocks that the system receives (e.g. shocks of consumer confidence that affect consumption). To see how the model works, consider two ...
Merton's portfolio problem is a problem in continuous-time finance and in particular intertemporal portfolio choice.An investor must choose how much to consume and must allocate their wealth between stocks and a risk-free asset so as to maximize expected utility.
Black–Litterman overcame this problem by not requiring the user to input estimates of expected return; instead it assumes that the initial expected returns are whatever is required so that the equilibrium asset allocation is equal to what we observe in the markets.
A capital recovery factor is the ratio of a constant annuity to the present value of receiving that annuity for a given length of time. Using an interest rate i, the capital recovery factor is: = (+) (+)
In this equilibrium, relative supplies will equal relative demands: given the relationship of price with supply and demand, since the risk-to-reward ratio is "identical" across all securities, proportions of each security in any fully-diversified portfolio would correspondingly be the same as in the overall market.
Tobin's q [a] (or the q ratio, and Kaldor's v), is the ratio between a physical asset's market value and its replacement value.It was first introduced by Nicholas Kaldor in 1966 in his paper: Marginal Productivity and the Macro-Economic Theories of Distribution: Comment on Samuelson and Modigliani.