E quity risk-based strategies are systematic quantitative approaches to stock allocation that rely only on risk views to manage risk and increase diversification. These strategies do not require any explicit stock return forecasts. The portfolios are periodically rebalanced to take into account drift and changes in risk views.The simplest of these strategies is based on the equally weighed (EW) portfolio that simply follows the principle of not putting all your eggs in one basket. The portfolio invests the same amount in each stock. The strategy makes sense if we believe that neither stock returns nor risk can be forecast.The equal-risk budget (ERB) strategy invests in portfolios with the same risk budget for each stock, which is defined as the product of the stock's weight and its volatility. Risk is equally distributed among the stocks and hence riskier stocks get smaller weights. This can be viewed as an extension of EW, if we trust volatility forecasts.If correlations are also taken into account, then we can think in terms of equal-risk contribution (ERC), where the contribution to risk from each stock is the same. Unlike the risk budget, the contribution to risk (defined as the product of the stock's weight and its marginal risk) 1 also takes into account the impact of correlations. The contribution to portfolio risk from two stocks with the same volatility but different correlations is higher for the stock with the higher correlation, and hence it gets a smaller weight in the ERC portfolio. The ERC strategy was discussed recently by Maillard, Roncalli, and Teiletche [2010].These three strategies assume diversification can be achieved by equally allocating wealth or risk across the investment universe. The two other risk-based strategies we analyze are different.Minimum variance (MV) invests in the portfolio with the lowest ex ante volatility. MV is the least risky approach to investing in equities and is expected to deliver the lowest volatility over time. It uses volatilities and correlations as inputs and should invest in stocks with the lowest volatility and low correlations.The maximum diversification (MD) strategy, introduced by Choueifaty and Coignard [2008], invests in the portfolio that maximizes a diversification ratio. The ratio is the sum of the risk budget allocated to each stock in the portfolio divided by the portfolio volatility. This strategy should invest in stocks that are less correlated to other stocks.

Analysis of portfolios formed with corporate high yield bonds in BofA Merrill Lynch indices ranked by DTY. January 2000 to December 2012. Monthly rebalancing. Value-weighted portfolios. All maturities, except for GBP bonds where maturity is capped at 15 years. 1 = lowest DTY. 5 = highest DTY. Δ(1-5) is the difference between statistics for #1 and #5 quintile portfolios.Analysis of portfolios formed with sovereign bonds in BofA Merrill Lynch indices ranked by DTY. January 1997 to December 2012. Monthly rebalancing. Value-weighted portfolios. All maturities. 1 = lowest DTY. 5 = highest DTY. Δ(1-5) is the difference between statistics for #1 and #5 quintile portfolios.

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