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A 60 / 30 / 10 portfolio of three funds: return, volatility, diversification benefit, drawdown and Value at Risk (illustrative data)

Tool	Portfolio Risk and Return
Source	Illustrative data: 60 months of synthetic returns drawn from a random-number generator (numpy, seed 1), not market data. Definitions: Markowitz, H. (1952). "Portfolio Selection." Journal of Finance, Vol. 7, No. 1, pp. 77–91; Sharpe, W. F. (1994). "The Sharpe Ratio." Journal of Portfolio Management, Vol. 21, No. 1, pp. 49–58; Value at Risk as defined in 12 CFR 3.202.
Level	Undergraduate

Problem

A portfolio holds 60 % in a stock fund, 30 % in a bond fund and 10 % in a gold fund, rebalanced every month. From 60 monthly returns of each fund, find the portfolio's annualised return and volatility, how much the mix lowers the volatility, the Sharpe and Sortino ratios against a 2 % risk-free rate, the maximum drawdown and the one-month 95 % Value at Risk and expected shortfall.

Inputs to Enter

60 monthly returns (percent) of Stock Fund, Bond Fund and Gold Fund, with a benchmark column Market (the form's default data, illustrative)
Weights 60, 30, 10 %; risk-free rate 2 % a year; confidence 95 %

Open the Portfolio Risk and Return tool (loaded with this example)

Answers

Growth of 1 over 5 years: 1.6184, annualised return 1.6184^(1/5) − 1 = 10.11 % (holdings 13.68 %, 1.69 %, 12.00 %)
Monthly standard deviation 2.639 %, annualised volatility 2.639 × √12 = 9.14 %; the same value from the weights, volatilities (14.18, 4.97, 12.61 %) and correlations (0.15, 0.13, 0.21)
Weighted-average volatility 11.26 %, diversification benefit 11.26 − 9.14 = 2.12 points
Sharpe ratio (0.840 − 0.165) / 2.639 × √12 = 0.89; downside deviation 1.533 % a month, Sortino ratio 1.52
Maximum drawdown −11.64 %, from 1.2989 at the end of month 26 to 1.1477 at the end of month 32
One-month 95 % Value at Risk: historical 3.02 % (expected shortfall 5.14 %), normal 1.645 × 2.639 − 0.840 = 3.50 % (expected shortfall 4.60 %)
Advanced mode, against the Market column: beta 0.584, alpha 3.91 % a year, tracking error 7.03 %, information ratio 0.13, up capture 72.1 %, down capture 49.0 %

Notes

The tool's default inputs are this case; press Submit. The data are made up for illustration, so the case teaches the method and says nothing about any real fund. Every value is checked against an independent numpy / pandas implementation (test_portfolio_risk_return.php).