Factor exposure and (Markowitz) diversification
Factor exposure and (Markowitz) diversification
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A general premise of Markowitz diversification is to diversify a portfolio so as to achieve a higher (expected) return for a given level of risk or lower risk for a given level of (expected) return. This is best achieved by combining assets with low correlation but similar expected return.
Here's an interesting example (at least to me) of diversification across factors (size, value, momentum). It considers two ways of getting exposure to positive momentum to add to a small value allocation through one of two approaches. Through S&P400 Midcap Growth which had a positive (and significant) momentum load (+0.10) since 1996, or more directly through the MSCI momentum index. Here are simulated results from 1996.
Annualized return and standard deviations since 1996.
15.6%/26.4 = RAFI Pure Small Value
13.4%/20.6 = S&P 400 MidCap Growth
12.0%/22.0 = MSCI Momentum
The S&P 400 MidCap Growth index had a 1.4% higher annualized return than the MSCI momentum index over this period, with lower standard deviation. Just for illustration, without trying to match factor loads, and considering a 25% allocation - which index provided greater diversification for the RAFI Pure Small Value Series? It turns out to be MSCI momentum (despite its lower return and higher standard deviation).
Annualized return/Standard deviation/Sharpe since 1996
15.3%/24.0/0.62 = 25% S&P 400 Midcap Growth:75% RAFI Pure Small Value
15.2%/23.0/0.64 = 25% MSCI Momentum:75% RAFI Pure Small Value
The reason: the average correlation over this period between RAFI Pure Small Value and S&P 400 Midcap Growth was 0.66, while with MSCI momentum it was 0.39. MSCI momentum provided more factor diversification (higher momentum load, lower size load), than S&P 400 Midcap Growth (lower momentum load, higher size load - the latter which had high correlation with the high size load on RAFI Pure Small Value). I think this is a good illustration (at least to me) of Markowitz diversification. Just to note the Sharpe ratios on the combined portfolios were higher than on S&P 400 Midcap Growth alone.
Robert
.
A general premise of Markowitz diversification is to diversify a portfolio so as to achieve a higher (expected) return for a given level of risk or lower risk for a given level of (expected) return. This is best achieved by combining assets with low correlation but similar expected return.
Here's an interesting example (at least to me) of diversification across factors (size, value, momentum). It considers two ways of getting exposure to positive momentum to add to a small value allocation through one of two approaches. Through S&P400 Midcap Growth which had a positive (and significant) momentum load (+0.10) since 1996, or more directly through the MSCI momentum index. Here are simulated results from 1996.
Annualized return and standard deviations since 1996.
15.6%/26.4 = RAFI Pure Small Value
13.4%/20.6 = S&P 400 MidCap Growth
12.0%/22.0 = MSCI Momentum
The S&P 400 MidCap Growth index had a 1.4% higher annualized return than the MSCI momentum index over this period, with lower standard deviation. Just for illustration, without trying to match factor loads, and considering a 25% allocation - which index provided greater diversification for the RAFI Pure Small Value Series? It turns out to be MSCI momentum (despite its lower return and higher standard deviation).
Annualized return/Standard deviation/Sharpe since 1996
15.3%/24.0/0.62 = 25% S&P 400 Midcap Growth:75% RAFI Pure Small Value
15.2%/23.0/0.64 = 25% MSCI Momentum:75% RAFI Pure Small Value
The reason: the average correlation over this period between RAFI Pure Small Value and S&P 400 Midcap Growth was 0.66, while with MSCI momentum it was 0.39. MSCI momentum provided more factor diversification (higher momentum load, lower size load), than S&P 400 Midcap Growth (lower momentum load, higher size load - the latter which had high correlation with the high size load on RAFI Pure Small Value). I think this is a good illustration (at least to me) of Markowitz diversification. Just to note the Sharpe ratios on the combined portfolios were higher than on S&P 400 Midcap Growth alone.
Robert
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Re: Factor exposure and (Markowitz) diversification
VTI Total US (being cap weighted of sorts) is somewhat like 92% VOO (S&P500) combined with 8% or so small. Substituting VISVX (small cap value) for the small i.e. 92% VOO, 8% VISVX has produced very similar results to VTI (total market).
A index of all stocks will include all factors - there will for instance be some stocks that are in momentum within that. If you opt to deviate from the market weightings then you're predicting one style or factor will be more rewarding over the particular period you invest across - and potentially incur higher costs and effort to manage.
Higher expected return based on historic comparisons, is by no means an assurance of higher actual returns.
A index of all stocks will include all factors - there will for instance be some stocks that are in momentum within that. If you opt to deviate from the market weightings then you're predicting one style or factor will be more rewarding over the particular period you invest across - and potentially incur higher costs and effort to manage.
Higher expected return based on historic comparisons, is by no means an assurance of higher actual returns.
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Re: Factor exposure and (Markowitz) diversification
Clive
Two problems IMO
1)An index of all stocks has only exposure to beta and NO OTHER FACTORS. That's a common mistake
2) while there is no guarantee of course that these factors will provide higher returns, saying that is no different than saying beta (the market) has no guarantee of higher expected returns. The best we can do is to use the evidence of high persistence and pervasiveness of a factor to make an intelligent decision on whether to add it or not to a portfolio
Robert
Another good example of why one should never look at things in isolation, only the whole matters
Larry
Two problems IMO
1)An index of all stocks has only exposure to beta and NO OTHER FACTORS. That's a common mistake
2) while there is no guarantee of course that these factors will provide higher returns, saying that is no different than saying beta (the market) has no guarantee of higher expected returns. The best we can do is to use the evidence of high persistence and pervasiveness of a factor to make an intelligent decision on whether to add it or not to a portfolio
Robert
Another good example of why one should never look at things in isolation, only the whole matters
Larry
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Re: Factor exposure and (Markowitz) diversification
Clive
Two problems IMO
1)An index of all stocks has only exposure to beta and NO OTHER FACTORS. That's a common mistake.The positive momentum stocks in TSM exactly offset the negative momentum stocks giving you no NET exposure to the factor. Same for all factors except beta.
2) while there is no guarantee of course that these factors will provide higher returns, saying that is no different than saying beta (the market) has no guarantee of higher expected returns. The best we can do is to use the evidence of high persistence and pervasiveness of a factor to make an intelligent decision on whether to add it or not to a portfolio
Robert
Another good example of why one should never look at things in isolation, only the whole matters
Larry
Two problems IMO
1)An index of all stocks has only exposure to beta and NO OTHER FACTORS. That's a common mistake.The positive momentum stocks in TSM exactly offset the negative momentum stocks giving you no NET exposure to the factor. Same for all factors except beta.
2) while there is no guarantee of course that these factors will provide higher returns, saying that is no different than saying beta (the market) has no guarantee of higher expected returns. The best we can do is to use the evidence of high persistence and pervasiveness of a factor to make an intelligent decision on whether to add it or not to a portfolio
Robert
Another good example of why one should never look at things in isolation, only the whole matters
Larry
Re: Factor exposure and (Markowitz) diversification
Take a look at Low Vol with SCV. Both USMV and SPLV have MOM of around 0.30 - 0.50 and both actually load positive on Value as well (particularly SPLV), instead of negative (as does MTUM). If you combine 50/50 with PXSV or RZV you have about the same return/SD and Sharpe as TSM. However, data are limited to just the last couple years. Let's assume those loadings hold up. Would it be worth splitting beween Low Vol and SCV do you think?
We don't know where we are, or where we're going -- but we're making good time.
Re: Factor exposure and (Markowitz) diversification
Browser, I think is a short term artefact, MOM of LowVol strategies. Have a look at Table 5 here: http://goo.gl/GlFcMJ
Or at http://papers.ssrn.com/sol3/papers.cfm? ... id=2298117
Or at http://papers.ssrn.com/sol3/papers.cfm? ... id=2298117
Abstract:
This paper replicates various low volatility strategies and examines their historical performance using U.S., global developed markets, and emerging markets data. In our sample, low volatility strategies outperformed their corresponding cap-weighted market indices due to exposure to the value, betting against beta (BAB), and duration factors. (The duration factor introduced here is new to the low volatility literature.) The reduction in volatility is driven by a substantial reduction in the portfolios’ market beta. For long-term investors, low volatility strategies can contribute to a more risk-diversified equity portfolio which earns equity returns from multiple premium sources instead of market beta alone. Nonetheless, while the lower risk and higher return seem persistent and robust across geographies and over time, we find flaws with naïve constructions of low volatility portfolios. First, naïve low volatility strategies tend to have very high turnover and low liquidity, which can erode returns significantly. They also have very concentrated country/industry allocations, which neither provide sensible economic exposures nor find theoretical support in the more recent literature on the within-country/industry low volatility effect. Additionally, there is concern that low volatility stocks could become expensive, a development which would eliminate their performance advantage. Portfolio construction methods should be sensitive to valuation levels and investability.
Re: Factor exposure and (Markowitz) diversification
You could cover a lot of bases with the authors' comments; for example:
First, naïve low volatility small cap value strategies tend to have very high turnover and low liquidity, which can erode returns significantly. They also have very concentrated country/industry allocations, which neither provide sensible economic exposures
Additionally, there is concern that low volatility small cap value stocks could become expensive, a development which would eliminate their performance advantage. Portfolio construction methods should be sensitive to valuation levels and investability.
We don't know where we are, or where we're going -- but we're making good time.
Re: Factor exposure and (Markowitz) diversification
Sure - aside from the turnover thing, which is not "very high" for SV. And there is another difference: Low beta seems to be a riskfree anomaly that should no be there. SV at least has some risk component which cannot be arbitraged away, though returns may be lower going forward. It also can be overcrowded from time to time, no doubt. Maybe it is at the moment. But note that the (U.S.) stock market (factor), as a slice and dice of the (global) capital market as a hole, is vulnerable to the same problem; flood of money, higher prices, lower future returns. So us the bond market, every bond sub asset class (e.g. treasuries, HY), REITS, real estate, ... Maybe the US stock market is overcrowded too at the moment, maybe not. SV? Maybe, maybe not. I don't really get your point in this threads, Browser? You seem to constantly jump between interest in tilts and TSM. Just pick a reasonable, low cost strategy and execute it for some decades. The only major difference is drawdown risk vs. underperformance risk anyway.
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Re: Factor exposure and (Markowitz) diversification
Browser, disagree with your last post.
First, small value is not a very high turnover strategy, it's higher than the market, but not high like MOM say. Also one can implement in a patient trading way so the relatively small amount of increased turnover will not have much impact on total costs.
Second, while you can have low vol stocks rise in price so they have negative expected premiums, that isn't the case with small value because of construction--it's always the 30% lowest prices by some metric (or whatever percentage is used), which means only that the premium can shrink but should not disappear
Larry
First, small value is not a very high turnover strategy, it's higher than the market, but not high like MOM say. Also one can implement in a patient trading way so the relatively small amount of increased turnover will not have much impact on total costs.
Second, while you can have low vol stocks rise in price so they have negative expected premiums, that isn't the case with small value because of construction--it's always the 30% lowest prices by some metric (or whatever percentage is used), which means only that the premium can shrink but should not disappear
Larry