# Adjusting volatility while constructing portfolio

I am trying to construct a portfolio based on a macro momentum strategy for backtesting purposes as outlined in https://www.aqr.com/-/media/AQR/Documents/Insights/White-Papers/A-Half-Century-of-Macro-Momentum.pdf.

So after constructing a long-short portfolio, the author outlines the following "I then volatility-adjust the resulting long and short positions such that the long-short portfolio is at 10% annual forecasted volatility using a three-year rolling risk model on monthly returns."

I am not from a finance background so if someone can please explain what does that mean, it would be really helpful. Please see page 20 in the pdf for more details.

If you think the question is badly framed then please suggest edits.

Thanks.

• A long short portfolio has a certain amount of leverage with respect to the capital employed, which is up to you to decide. The authors selected the amount of leverage so the standard deviation of the portfolio gains/losses is equal to 10% of the capital. (This is a very standard step in designing any long/short strategy). Nov 13, 2019 at 18:59
• Hi Alex, can you please share any source where I can learn the math behind the designing long/short portfolio strategy? Thanks. Nov 18, 2019 at 7:54
• Moreira and Muir: Volatility Managed Portfolios is the one I like. But Develarist below hs many more. Nov 18, 2019 at 20:52
• Thank you Alex :) Nov 20, 2019 at 4:32

Page 6 also describes

Long-short portfolios take long (or short) positions in assets with favorable (or unfavorable) macroeconomic trends relative to the cross-sectional average, and are designed to be market neutral at all points in time.

Combined with the quote you found, I think there is math behind his approach that isn't shared in the write-up, but sounds alot like the Risk Parity approach, especially Volatility Targeting portfolios, where the overall portfolio volatility is targeted to be some value (10%) for the chosen time horizon settings. Step-wise, targeting the overall portfolio volatility is usually a shell outside the actual estimation and transformation of individual portfolio weights. There is no math anywhere so it can be anyone's guess how the numbers are obtained.

Besides the minimum variance and maximum diversification portfolios, other common portfolio risk optimization techniques include:

• Risk parity portfolio

Maillard, S., T. Roncalli, andj. Teiletche. “The Properties of Equally Weighted Risk Contribution Portfolios.” The Journal of Portfolio Management, Vol. 36, No. 4 (2010), pp. 60-70.

Chaves, D., J. Hsu, F. Li, and O. Shakernia. “Risk Parity Portfolio versus Other Asset Allocation Heuristic Portfolios.” The Journal of Investing, Vol. 20, No. 1 (2011), pp. 108-108.

Asness, C., A. Frazzini, and L. Pedersen. “Leverage Aversion and Risk Parity.” Financial Analysts Journal, Vol. 68, No. 1 (2012), pp. 47-59.

• Volatility targeting portfolio

Busse,J. “Volatility Timing in Mutual Funds: Evidence from Daily Returns.” Review of Financial Studies, Vol. 12, No. 5 (1999), pp. 1009-1041.

Collie, R., M. Sylvanus, and M. Thomas. “Volatility- Responsive Asset Allocation.” White paper, Russell Investments, 2011.

Butler, A., and M. Philbrick. “Volatility Management for Better Absolute and Risk-Adjusted Performance.” White paper, Macquarie Private Wealth Inc., 2012.

Albeverio, S., V. Steblovskaya, and K. Wallbaum. “Investment Instruments With Volatility Target Mechanism.” Quantitative Finance, Vol. 13, No. 10 (2013), pp. 1519-1528.

• Thanks for confirming my doubts. I was guessing there's maths behind this which the author did not show. Can you please point me to any source where I can learn the concepts you mentioned regarding portfolio construction. Thanks. Nov 18, 2019 at 7:52
• sources for the portfolio risk optimization techniques mentioned have been added above Nov 18, 2019 at 20:40
• Thank you so much @develarist Nov 20, 2019 at 4:32