Tools › Investing › Portfolio and Risk

Portfolio and Risk

9 tools in the Investing area.

Portfolio Risk and Return

Risk and return of a portfolio from the returns or prices of its holdings, with every step shown. Paste one column per holding, enter the weights, and the page works out the annualized return, the volatility, the Sharpe and Sortino ratios, the maximum drawdown, the correlation between the holdings, how much diversification lowers the volatility, and the one-period Value at Risk and expected shortfall. Advanced mode compares the portfolio with a benchmark column. A calculator for education and analysis, not investment advice.

1 worked example reproduced, listed on the tool page.

Efficient Frontier

Mean-variance portfolios of up to twelve holdings by Markowitz's method, with the steps shown. From typed expected returns, volatilities and correlations, or from pasted returns, the page finds the minimum-variance portfolio, the maximum-Sharpe (tangency) portfolio and the efficient frontier, long-only or with shorting and with an optional maximum weight, and draws them with the capital market line. Equal-weight and risk-parity portfolios are listed beside them, and a sensitivity table shows how far the weights move when one expected return changes by a point. A calculator for education and analysis, not investment advice.

1 worked example reproduced, listed on the tool page.

Factor Exposure

Measures how a fund's or portfolio's returns have moved with a set of factor returns, step by step. Paste the returns beside the factor returns; the page first fits the single-factor (market) line by hand, then the multi-factor regression with the standard error, t statistic, p-value and 95 % interval of every loading, the annualized alpha, R-squared, the volatility the factors leave unexplained and the share of variance attributed to each factor. A calculator for education and analysis, not investment advice.

1 worked example reproduced, listed on the tool page.

Portfolio Rebalancing

What to buy and sell to bring a portfolio back to its target mix. Enter each holding with its current value and its target percent, any new cash to add (or a withdrawal as a negative amount), and choose a full rebalance (buy and sell) or new cash only (no sales). The page shows the current weights and how far each has drifted from its target, works out each trade step by step, lists the value and weight of every holding after the trades and the total amount traded; with new cash only it fills the most underweight holding first and shows the drift that remains. Advanced mode adds share prices for whole-share trades with the cash left over, a tolerance band that trades only the holdings outside it, an estimate of the tax on the sales from each holding's cost basis, and a trading cost. No market data is used: every value is typed in. A calculator for education and analysis, not investment advice.

1 worked example reproduced, listed on the tool page.

Position Size and Risk

How many shares to buy so that being stopped out loses a chosen amount. Enter the account size, the percent of it risked on one trade, the entry price and the stop price; the page works out step by step the money at risk, the risk per share, the number of shares, the value of the position and its share of the account. With a target price and a win rate it adds the reward-to-risk ratio, the win rate at which that ratio breaks even and the expectancy per trade. Advanced mode adds a stop set by volatility, commission and slippage, short positions, the chance of a chosen fall in the account over a run of trades by simulation, the longest losing streak to expect and the Kelly fraction beside the entered risk. A calculator for education and analysis, not investment advice.

1 worked example reproduced, listed on the tool page.

Kelly Criterion

The Kelly criterion for a repeated opportunity with a known payoff: the probability the quoted payoff implies, the edge against your own estimate of the true probability, the expected value of a unit stake, the Kelly fraction that maximizes the long-run growth of capital and the fractional Kelly stake used in practice, and a Monte Carlo simulation of the capital over a series of trials showing the median path, the spread and the chance of a deep drawdown. The payoff may be entered in moneyline, decimal or fractional form.

Portfolio Backtest

How a fixed-weight portfolio would have done on your own price history, with every step shown. Paste one column of prices or returns per asset, enter the weights, the starting amount, a contribution or withdrawal per period and a rebalancing rule. The page follows the portfolio period by period and reports the ending value, the time-weighted and money-weighted yearly returns, the volatility, the deepest drawdown with its dates, the best and worst year, the rebalancing trades and turnover, the same portfolio under each rebalancing rule side by side, and how much each asset added. A backtest describes the past sample only. A calculator for education and analysis, not investment advice.

1 worked example reproduced, listed on the tool page.

Performance Attribution

Why did a portfolio beat or trail its benchmark? Enter each segment (a sector, a country, an asset class) with its weight and return in the portfolio and in the benchmark. The page works out the total return of each, the active return (portfolio less benchmark), and splits the active return segment by segment into three effects by the Brinson-Hood-Beebower method: allocation (holding more or less of a segment than the benchmark), selection (earning more or less than the benchmark inside a segment) and interaction (the two together). The Brinson-Fachler form of the allocation effect is shown beside it, the first segment is written out step by step, and the effects are added back up to the active return. Advanced mode folds interaction into selection, adds a cash segment, and links a second period with the Carino smoothing factors so that the effects add up to the compounded active return. No market data is used: every value is typed in. A calculator for education and analysis, not investment advice.

1 worked example reproduced, listed on the tool page.

Black-Litterman

The Black-Litterman model blends the returns implied by the market portfolio with an investor's own views, with the steps shown. From market weights, volatilities and correlations the page finds the implied equilibrium returns, turns up to four views (one asset, or one asset minus another) into the view matrices, sets the uncertainty of each view in proportion to its variance or from a stated confidence, and works the posterior returns, their uncertainty and the resulting weights beside the market weights, with a table of how the weights move as confidence rises from 0 to 100 %. The default case is the published example of Idzorek (2005). A calculator for education and analysis, not investment advice.

1 worked example reproduced, listed on the tool page.

Other Investing sections

Economy and Rates · Company Financials · Stock Valuation · Bonds · Options · Saving and Planning · Mergers and Buyouts · Private Markets