Portfolio Optimization Methods
For the first post of the publication we have chosen to explore a topic that is a prime topic of deliberation whenever one is trying to construct a multi asset portfolio. One can slice and dice any portfolio into component weights in countless ways, what then is the best strategy to follow when making this decision? In this article we will try to introduce the most widely used strategies and understand intuitively when to use them.
Common Methods
The most common portfolio weigh allotment technique is the market capitalization based weighing — which is employed by the major indices and consequently most of the passive funds. Otherwise the naive go to methods are — equal weighting or conviction based weighting. If one follows in the Capital Asset Pricing Mode or CAPM, the most elegant solution is the Markovitz Optimal portfolio. People also widely use the inverse volatility portfolios, equal-risk portfolios and the minimum variance portfolio.
If one has a strong multi-factor model is place then one can optimize the exposures of preferred factors and target volatility or turnover constraints.
Looking at the common portfolio construction methods —
When do we use which method?
Surely each of these methods could be of choice under different conditions contingent on different factors. So what are these factors?
Behavioral Factors
An investor with a risk averse outlook would favor a method that minimizes risk. Someone with a view on correlations would opt for maximum diversification. Someone who has very strong conviction on his ideas might choose a conviction based weighing.
Liquidity
The characteristic of highly liquid stocks might be quite similar and a beta weighting might make sense. Whereas, for illiquid stocks the volatility might be high and correlation low.
Volatility
For a set of assets with similar Sharpe ratios, the optimal portfolio would be the one weighted on asset volatility. When assets have similar returns but varying volatility, one might want to for inverse volatility weighting.
Correlation
For imperfectly correlated stocks, the portfolio returns and volatility are different from the weighted sum. So the correlation between the assets would effect the weighting mechanism in a large way.
Market Regimes
As markets transition from high variance to low variance regimes, the correlation patterns and asset risk return characteristics vary significantly. Which is why the portfolio weight choice would be a function of the market regimes.
Observations
With these ideas we experiment with these methods using S&P 500 component companies and see what works best when. We use following test sets — large cap stocks, small cap stocks, highly correlated stocks and low correlation stocks and see what performs best for each of these test sets.
Large Cap Stocks
We can see here that minimum variance works best, followed by the max diversification portfolio. The equal risk portfolio gives the worst returns.
Small Cap Stocks
Here equal risk weighing works best followed by market cap weighting, max diversification portfolio gives the worst results.
High Correlation
Here inverse variance and inverse volatility weighing work best, max diversification portfolio gives the worst results. Mean variance and min variance have high returns but low Sharpe.
Low Correlation
Here market cap weighing and inverse variance work best, max diversification and mean variance optimal portfolio give the worst results.
We can see that different portfolio construction methods give different performance for different asset sets which emphasizes the importance of understanding of asset and market characteristics as well as the principals of the portfolio construction methodologies.
We would like to cite “Portfolio Optimization: A General Framework for Portfolio Choice” by Resolve Asset Management that we were highly inspired by.
