Minimum Variance Portfolio: Important Things to Know
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The importance of diversification, asset allocation, and portfolio construction can not be overstated.
A buy and hold strategy of low-cost index funds (or ETFs) is generally superior to picking individual stocks (and a smarter way to build wealth).
Throughout it all, you may have heard the term minimum variance portfolio tossed around.
What on earth is that?
Minimum Variance Portfolio is the technical way of representing a low-risk portfolio.
It carries low volatility as it correlates to your expected return (you’re not assuming greater risk than is necessary).
Obviously, a one line description won’t be enough to satisfy all doubts.
In this post, we’re going to talk about what a minimum variance portfolio is, examples of how to build one, and why it’s a useful risk management tool.
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Minimum Variance Portfolio 101: Getting Started
What Is A Minimum Variance Portfolio?
A minimum variance portfolio holds individual, volatile securities that aren’t correlated with one another.
One security might be surging in value while another is plummeting, it doesn’t matter. Because of their low correlation, the portfolio as a whole is viewed as less risky.
But how?
Let’s go deeper.
Any two investments with a low correlation to each other can form a minimum variance portfolio (e.g., stocks and bonds).
Variance is a measurement of risk. There’s a lot of math’s behind it but simply put:
Variance measures the daily fluctuations of an investment. The more significant the change in price, the higher its variance, and more volatile.
For example, bonds have a lower volatility than stocks and low variance. The standard deviation of an investment is the square root of the variance – both measure portfolio risk.
When people talk about what a wild ride the stock market is, that’s what they mean.
One day your stock is up 24%, the next it’s down -5%.
However, if you take a snapshot of the Dow from 1900 through the present, you will notice that the market always goes up.
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What is Correlation?
Correlation measures movements between investments. It’s kind of like watching two people on a date.
Sometimes, they’re in sync, move in lockstep, and finish each other’s sentences. Other times, well, let’s just say it isn’t like that at all.
For example, if two assets are negatively correlated, they’ll move in opposite directions, like a date gone bad.
While you are trying to implement a minimum variance portfolio, you should look for investments with low to negative correlation. You should look for diversification across asset classes.
What is Diversification?
Harry Markowitz, Modern Portfolio Theory, and the Efficient Frontier
Harry Markowitz’s work in the 1950s won him a Nobel Prize and has become a cornerstone for modern portfolio construction. Notable accolades include:
- Nobel Prize recipient in Economics
- During his doctoral days at the University of Chicago, Markowitz’s Ph.D. dissertation helped him write his book Portfolio Selection.
- Designed a computer language at RAND Corporation
- Hedge Fund Manager
- Acorns Investment Committee Advisor
Henry Markowitz explained MPT as a rating of two measurements:
- Volatility
- Expected return
At its core, MPT seeks to lower portfolio volatility through diversification while increasing your return. As investors, that’s the dream.
According to the Modern portfolio theory, choosing asset classes with low to negative correlation such as stocks and bonds can lead to a reduction in portfolio variance.
The Efficient Frontier
The Efficient Frontier is a graph that rates your portfolio’s risk (x-axis) versus return (y-axis). It shows you the amount of profit you should expect from an assumed level of risk.
It’s not the risk factor of an individual stock that matters, it’s actually how the stock affects the risk factor of your entire portfolio that determines whether you should invest or not.
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Not all portfolios operate as efficiently as they could, and not all investments are created equal.
The reason behind that is the fact that there’s only a certain amount of accepted risk you can take before your investment portfolio becomes sub-optimal (i.e., too much risk, not enough return).
Portfolios landing to the right and below the efficient frontier are viewed as inferior because the expected return is too low for the level of risk taken.
In a nutshell, an efficient portfolio (or a portfolio falling on the efficient frontier) offers the best return you can expect for the degree of volatility you’re taking on.
It’s an outgrowth of MPT. Because there’s an infinite number of security combinations producing varying levels of return, the efficient frontier represents the best of those combinations.
One school of thought suggests investors pivot from an efficient portfolio to a minimum variance portfolio as they near retirement.
Highly-diversified portfolios tend to hold a place along the efficient frontier.
Minimum Variance Portfolios In Action
Take this simple example: Imagine you’ve got a single asset class. Let’s say it’s a stock in an emerging market index fund.
That index fund alone is highly volatile. 100% invested in emerging market stocks is a risky play.
But if you throw in small-cap, total international, and large-cap stocks, (split evenly four ways) you’ve reduced your risk through diversification.
For example, a small-cap and an international stock won’t always move in sync with each other. If international goes down, the other three won’t be as affected.
You’ve just added four volatile, low-correlated investments to your portfolio while lowering risk.
An alternative would be to hold a percentage of bonds in your portfolio.
Remember, having investments with low correlation is the key ingredient to a Minimum Variance Portfolio (MVP).
However, when you turn your focus towards individual stocks within specific sectors and buy on margin, the strategy becomes extremely complicated.
Individual investors, particularly beginners, will want to steer clear. However, if you are curious enough, let’s find out more about it.
Minimum Variance and Risk Parity
Another way to maximize returns is through leverage. Rather than stuff your portfolio with risky assets, an alternative is to balance your portfolio with safer securities.
Now, you have the option to borrow against your low volatility portfolio. This can help you maximize your returns with the help of Risk Parity.
Billionaire hedge fund investor and manager Ray Dalio coined the investment strategy at his firm, Bridgewater.
It says that riskier assets are overpriced with sub-par returns. In a nutshell, you’re accepting higher volatility for less reward.
It also means that safer assets will get you superior returns considering the lower level of risk assumed.
You’re borrowing against your portfolio and investing heavier in low-risk securities.
When you increase your leverage in the minimum variance portfolio, your potential earnings can increase without the use of risky assets.
The Sharpe Ratio: A Risk Management Tool
Measuring Return and Risk
It makes sense to start from a risk-based approach. Past performance doesn’t guarantee future results.
However, financial analysts still wanted to make sense of it all. Sharpe ratio is a way to combine an investment’s risk and return into one statistic.
We already know that the standard deviation is a way to measure portfolio volatility.
Then William Sharpe discovered a calculation that accounts for both risk and return, aptly named The Sharpe Ratio.
He’s also a Nobel Prize recipient for his work in the creation of the capital asset pricing model (CAPM) which says there are two types of risk:
- Systematic (Market) risk can’t be diversified away (e.g., the day-to-day gyrations of stock prices due to interest rates, inflation, etc.)
- Unsystematic (Specific) risk consists of factors unique to a particular company and can be diversified away (e.g., a company’s CEO is charged with doctoring the books and goes out of business, natural disasters, labor strikes, etc.)
Takeaway: Market risk can’t be removed through diversification and is the type of risk investors are rewarded for.
Mathematical Explanation
The Sharpe Ratio in action looks like this:
Risk ⁄ Return
For example, if you have an investment with an expected return of .10 and a standard deviation of .30, you’d have this:
.10/.30 = .33
Now imagine there’s a second investment with the same expected return of 10%, but a standard deviation of .50:
.10/.50 = .20
The investment with the higher Sharpe Ratio wins because you’re getting the same return for less risk.
The fact that Sharpe Ratio is absolute and not relative to a benchmark makes it really special.
It tells you how much risk you’re shouldering for the return.
To reduce the amount of risk associated with a reward, investments with higher Sharpe Ratios come really handy.
Minimum Variance Portfolio: Conclusion
Portfolio optimization gets complicated fast. While minimum variance portfolios are important, your asset allocation is what matters most.
Constructing your portfolio with a few low-cost index funds (or ETFs) and embracing a buy and hold strategy will lead you to long-term wealth with fewer headaches.
A lower risk investment portfolio thanks to diversification and low (or non) correlated securities, this is the essence of minimum variance.
Interesting read: What is a Factor Based Portfolio?
Investors chasing higher returns through advanced strategies with little understanding usually run into trouble. Keep it simple.
Invest within the basic asset classes that you know (stocks, bonds, cash etc.).
You’ll still have your minimum variance portfolio, just a simpler one. And the simpler solution is always best.
But if you’re ready to jump into the deep end of the pool, go for it! If done right, it can potentially enhance your returns.
