Comparing Portfolio Risk and Return with CAPM and Portfolio Tests
Summary
The discussion compares high-beta and low-beta equity portfolios and asks how to judge their risk-adjusted performance. Under CAPM assumptions, an investor can combine the market portfolio with borrowing or lending at the risk-free rate to reach a preferred point along the capital market line. If leverage is unavailable, an equity portfolio with a different beta may be considered, though the response argues that a low-beta portfolio may be less attractive than holding the market with risk-free assets.
Suggested comparisons include Sharpe or Treynor ratios, while recognizing that turnover and transaction costs can affect practical results. The discussion also recommends optimizing the complete portfolio rather than judging its components separately, and proposes simulation or backtesting when a direct choice is required. One answer cites empirical claims that low- and medium-beta portfolios have outperformed high-beta portfolios on a risk-adjusted basis, but offers no supporting study details. The guidance depends on assumptions about CAPM, borrowing access, efficient portfolios, historical distributions, and individual risk tolerance; it does not establish a universally superior portfolio.
Key ideas
- Under CAPM assumptions, investors can adjust market exposure by combining the market portfolio with borrowing or lending at the risk-free rate.
- Sharpe and Treynor ratios are possible measures for comparing portfolio risk and return.
- Turnover, transaction costs, borrowing costs, and leverage limits can change a portfolio comparison.
- Portfolio optimization should account for the full portfolio rather than evaluating holdings in isolation.
- Simulation and backtesting can inform a choice, but historical data and risk preferences limit what they establish.
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Full text
# Given two portfolios with identical correlation matrices, which one will have a better risk/reward ratio?
# Given two portfolios with identical correlation matrices, which one will have a better risk/reward ratio?
I have one portfolio with high beta stocks, and one with low beta stocks. Is it better to have higher expected return with high volatility, or medium expected return with medium volatility? (All from a asset allocation, efficient frontier, risk/reward prospective.)
## Answer by Richard Herron (score 6)
https://quant.stackexchange.com/a/861
From a theoretical point of view (you mentioned beta, so assume we're in a CAPM world), you should hold the market portfolio (let's assume S&P500 index) and be long (or short) the risk-free asset to decrease (or increase) your return and risk. That is, if you'd like higher returns than the S&P500 offers and are willing to accept the risk, trade the S&P500 index on margin. Again, theoretically, you want to hold a portfolio along the line tangent to the efficient frontier.
In the real world, maybe you can't lever up and trade on margin (maybe borrowing from the bank to buy an S&P500 index fund), so then you'd want to look at an equity only portfolio with a beta greater than one.
If you're looking at portfolio with a beta below one, then it seems that you should just hold the market and risk-free debt (maybe a money market savings account or low-yield corporate debt index fund, depending on your liquidity needs), which should outperform your low beta portfolio for a given level of risk.
Assuming that you've minimized risk for a given return (i.e., you're on the efficient frontier), then ultimately your risk aversion will determine your trade off between risk and return (i.e., picking the right beta). I agree with Chris that the Sharpe and Treynor ratios are good ways of quantifying the risk-return trade-offs in each of these portfolios.
Although not viewed as rational in the strict sense, given that you likely need this capital for retirement or buying a house, you may want to also look at value-at-risk (VaR) or expected shortfall (ES) to quantify how much you could lose in some hypothesized worst-case scenario. Of course, there are some problems with these measures, but they're illustrative.
## Answer by chrisaycock (score 5)
https://quant.stackexchange.com/a/858
Most portfolio managers look at the Sharpe ratio, or occasionally the Treynor ratio. In general, you want to maximize one of the these metrics, though there could be other issues that you haven't currently considered, like turnover or transaction costs associated with obtaining the portfolio.
## Answer by Joshua Chance (score 4)
https://quant.stackexchange.com/a/863
The empirical evidence shows that low to medium beta portfolios beat high beta portfolios on a risk adjusted basis. Search SSRN for "betting against beta." This flies completely in the face of CAPM but frankly CAPM is crap.
## Answer by DeepSpace101 (score 2)
https://quant.stackexchange.com/a/4907
You still want to perform portfolio optimization. Put everything into one bucket, run 'global' portfolio optimization, build the portfolio. Even if you prefer Sharpe ratios, you should do that on the overall portfolio - not just on individual ones. Be careful of sharpe ratios for low risk, low return assets. Dividing one small number by another small number can sometimes give you a giant number and you can't always lever that up as you please (you hit the friction of overleverage => higher borrowing rate)
Now if you must pick only one over the other (I'm assuming you've questioned why this limitation applies to you), then you should run a monte carlo simulation or perform some back testing of both portfolios. In a temporal way, the world is similar (same management, similar human attributes etc) but not exact (tech bust won't be exactly played out next time). Therefore I prefer Monte Carlo (using historical distributions from which to draw simulation outcomes) over straight up back testing ("In 2001, this portfolio would have looked like ...")Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.