The net present value (NPV) or net present worth (NPW) applies to a series of cash flows occurring at different times. The present value of a cash flow depends on the interval of time between now and the cash flow. It also depends on the discount rate. NPV accounts for the time value of money. It provides a method for evaluating and comparing capital projects or financial products with cash flows spread over time, as in loans, investments, payouts from insurance contracts plus many other applications.
In finance, the capital asset pricing model (CAPM) is a model used to determine a theoretically appropriate required rate of return of an asset, to make decisions about adding assets to a well-diversified portfolio.
The Modigliani–Miller theorem is an influential element of economic theory; it forms the basis for modern thinking on capital structure. The basic theorem states that in the absence of taxes, bankruptcy costs, agency costs, and asymmetric information, and in an efficient market, the enterprise value of a firm is unaffected by how that firm is financed. This is not to be confused with the value of the equity of the firm. Since the value of the firm depends neither on its dividend policy nor its decision to raise capital by issuing stock or selling debt, the Modigliani–Miller theorem is often called the capital structure irrelevance principle.
In finance, the duration of a financial asset that consists of fixed cash flows, such as a bond, is the weighted average of the times until those fixed cash flows are received. When the price of an asset is considered as a function of yield, duration also measures the price sensitivity to yield, the rate of change of price with respect to yield, or the percentage change in price for a parallel shift in yields.
In finance, the Sharpe ratio measures the performance of an investment such as a security or portfolio compared to a risk-free asset, after adjusting for its risk. It is defined as the difference between the returns of the investment and the risk-free return, divided by the standard deviation of the investment returns. It represents the additional amount of return that an investor receives per unit of increase in risk.
The Sortino ratio measures the risk-adjusted return of an investment asset, portfolio, or strategy. It is a modification of the Sharpe ratio but penalizes only those returns falling below a user-specified target or required rate of return, while the Sharpe ratio penalizes both upside and downside volatility equally. Though both ratios measure an investment's risk-adjusted return, they do so in significantly different ways that will frequently lead to differing conclusions as to the true nature of the investment's return-generating efficiency.
The Treynor reward to volatility model, named after Jack L. Treynor, is a measurement of the returns earned in excess of that which could have been earned on an investment that has no diversifiable risk, per unit of market risk assumed.
The drawdown is the measure of the decline from a historical peak in some variable.
In probability theory, the Kelly criterion, is a formula that determines the optimal theoretical size for a bet. It is valid when the expected returns are known. The Kelly bet size is found by maximizing the expected value of the logarithm of wealth, which is equivalent to maximizing the expected geometric growth rate. It was described by J. L. Kelly Jr, a researcher at Bell Labs, in 1956. The criterion is also known as the scientific gambling method, as it leads to higher wealth compared to any other strategy in the long run.
In finance, return is a profit on an investment. It comprises any change in value of the investment, and/or cash flows which the investor receives from that investment, such as interest payments, coupons, cash dividends, stock dividends or the payoff from a derivative or structured product. It may be measured either in absolute terms or as a percentage of the amount invested. The latter is also called the holding period return.
The information ratio, also known as appraisal ratio, measures and compares the active return of an investment compared to a benchmark index relative to the volatility of the active return. It is defined as the active return divided by the tracking error. It represents the additional amount of return that an investor receives per unit of increase in risk. The information ratio is simply the ratio of the active return of the portfolio divided by the tracking error of its return, with both components measured relative to the performance of the agreed-on benchmark.
In finance, diversification is the process of allocating capital in a way that reduces the exposure to any one particular asset or risk. A common path towards diversification is to reduce risk or volatility by investing in a variety of assets. If asset prices do not change in perfect synchrony, a diversified portfolio will have less variance than the weighted average variance of its constituent assets, and often less volatility than the least volatile of its constituents.
The ulcer index is a stock market risk measure or technical analysis indicator devised by Peter Martin in 1987, and published by him and Byron McCann in their 1989 book The Investors Guide to Fidelity Funds. It is designed as a measure of volatility, but only volatility in the downward direction, i.e. the amount of drawdown or retracement occurring over a period.
Post-modern portfolio theory is an extension of the traditional modern portfolio theory. Both theories propose how rational investors should use diversification to optimize their portfolios, and how a risky asset should be priced.
The modified Dietz method is a measure of the ex post performance of an investment portfolio in the presence of external flows.
Modigliani risk-adjusted performance (also known as M2, M2, Modigliani–Modigliani measure or RAP) is a measure of the risk-adjusted returns of some investment portfolio. It measures the returns of the portfolio, adjusted for the risk of the portfolio relative to that of some benchmark (e.g., the market). We can interpret the measure as the difference between the scaled excess return of our portfolio P and that of the market, where the scaled portfolio has the same volatility as the market. It is derived from the widely used Sharpe ratio, but it has the significant advantage of being in units of percent return (as opposed to the Sharpe ratio – an abstract, dimensionless ratio of limited utility to most investors), which makes it dramatically more intuitive to interpret.
The risk-return ratio is a measure of return in terms of risk for a specific time period. The percentage return (R) for the time period is measured in a straightforward way:
The V2 ratio (V2R) is a measure of excess return per unit of exposure to loss of an investment asset, portfolio or strategy, compared to a given benchmark.
The public market equivalent (PME) is a collection of performance measures developed to assess private equity funds and to overcome the limitations of the internal rate of return and multiple on invested capital measurements. While the calculations differ, they all attempt to measure the return from deploying a private equity fund's cash flows into a stock market index.
The Rachev Ratio is a risk-return performance measure of an investment asset, portfolio, or strategy. It was devised by Dr. Svetlozar Rachev and has been extensively studied in quantitative finance. Unlike the reward-to-variability ratios, such as Sharpe ratio and Sortino ratio, the Rachev ratio is a reward-to-risk ratio, which is designed to measure the right tail reward potential relative to the left tail risk in a non-Gaussian setting. Intuitively, it represents the potential for extreme positive returns compared to the risk of extreme losses, at a rarity frequency q defined by the user.
