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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.
Under the assumption of normality of returns, an active risk of x per cent would mean that approximately 2/3 of the portfolio's active returns (one standard deviation from the mean) can be expected to fall between +x and -x per cent of the mean excess return and about 95% of the portfolio's active returns (two standard deviations from the mean) can be expected to fall between +2x and -2x per ...
Profitability index (PI), also known as profit investment ratio (PIR) and value investment ratio (VIR), is the ratio of payoff to investment of a proposed project.It is a useful tool for ranking projects because it allows you to quantify the amount of value created per unit of investment.
Example of the optimal Kelly betting fraction, versus expected return of other fractional bets. In probability theory, the Kelly criterion (or Kelly strategy or Kelly bet) is a formula for sizing a sequence of bets by maximizing the long-term expected value of the logarithm of wealth, which is equivalent to maximizing the long-term expected geometric growth rate.
In general, when there are portfolio constraints – for example, when short sales are not allowed – the easiest way to find the optimal portfolio is to use the Black–Litterman model to generate the expected returns for the assets, and then use a mean-variance optimizer to solve the constrained optimization problem. [2]
The 5% Value at Risk of a hypothetical profit-and-loss probability density function. Value at risk (VaR) is a measure of the risk of loss of investment/capital.It estimates how much a set of investments might lose (with a given probability), given normal market conditions, in a set time period such as a day.
The assets in financial portfolios are, for practical purposes, continuously divisible while portfolios of projects are "lumpy". For example, while we can compute that the optimal portfolio position for 3 stocks is, say, 44%, 35%, 21%, the optimal position for a project portfolio may not allow us to simply change the amount spent on a project.
Where there is a budget constraint, the ratio of NPV to the expenditure falling within the constraint should be used. In practice, the ratio of present value (PV) of future net benefits to expenditure is expressed as a BCR. (NPV-to-investment is net BCR.) BCRs have been used most extensively in the field of transport cost–benefit appraisals.