Sunday, October 07, 2007

Advanced Portfolio Building II

A couple of days ago I wrote a detailed post I called Advanced Portfolio Building. As of now, that article received only a single comment, but I think that comment merits a detailed discussion and I will do so in this post. Let's begin by reviewing the full text of the comment, left by Matthew from Crazy Money:

"There are two methods for reducing volatility in a portfolio: building a basket of assets with weakly or anti-correlated betas, or increasing your time horizon. No discussion of risk and reward is complete without including the impact of time on both quantities.Given a sufficiently long window, there is no reason to invest in anything but 100% equities. Diversifying beyond this asset class would only create a drag on your final return and increase transaction costs.

I agree with some of the points Matthew is making in his well thought-out comment, but I strongly disagree with others. Clearly, Matthew is right that the longer your time horizon the more aggressive your portfolio can be. This is a basic truth of investing.

However, let's make a distinction between risk and expected return. Risk is traditionally measured by the volatility of the asset class in question. Volatility is the relative change in price over time. The concept of risk is strongly related to but is very different from the concept of expected return. Expected return is the amount of money you would receive, on average, over a certain period of time, by investing in that asset class. Let me give an example that will clarify the difference between those two concepts:

The S&P 500 for example has historically averaged a return of approximately 7.3% per year since its inception (not including dividends). If you believe that the S&P will continue to behave as it previously did, your expected return is about 7.3% per year (plus dividends). However, the S&P very rarely yields exactly 7.3%. The return fluctuates. Some years the S&P returns double digit gains, other years investors lose an arm, a leg and one buttock. The S&P (as well as all other equity) is a relatively volatile and hence risky asset class.

Given the option between a volatile asset and a stable asset, both of which are expected to return the same amount, a rational investor chooses the more stable asset. Why accept uncertainty and risk if in the end you expect to make the same amount of money? Think of it this way: if you were able to get 7.3% on a CD, every year, for the foreseeable future, would you invest in the S&P which on average would yield the same return, but could have some seriously down years included in the mix? Of course you wouldn't.

With the concepts of expected return and volatility safely locked in out heads, let's go back to Matthew's comment. Matthew is saying: "There are two methods for reducing volatility in a portfolio: building a basket of assets with weakly or anti-correlated betas, or increasing your time horizon". That statement is not correct. By increasing your time horizon you are more likely to achieve the expected average return on the asset class in which you are investing (7.3% in the example we used above), but you are doing NOTHING about volatility.

Let me explain: in any given year the stock market may tank or soar, but if you stay in the market for a large number of years, your chances of achieving your expected return are high. Compare it to a game of heads or tails. If you flip a coin twice, you wouldn't be surprised if it came up heads (or tails) twice. However, if you repeated that coin flip 1,000 times you would expect (and the laws of probability are on your side) that the number of heads and tails will be pretty close to each other. You would be really surprised if you threw heads 900 times and tails only 100 times - although that too COULD happen. This is because the expected outcome of the game is that 50% of the time you will flip a head, and 50% tails will appear. However, the long term expected outcome has absolutely no bearing on the next flip of the coin.

Matthew is confusing volatility with expected return. By expanding your time horizon you are likely to achieve the expected return, over the life of your investment, but that does not reduce the risk that your portfolio will tank in any given year.

Enter diversification: going back to the coin flipping game. Diversification is akin to playing heads or tails with several coins simultaneously. Each coin represents a different asset class in your portfolio. The chances of flipping all tails when using, say, 10 coins simultaneously is vanishingly small. Diversification reduces the volatility of your portfolio, and in many cases it can do so without reducing your expected return. Matthew's statement that "Diversifying beyond this asset class [equity - Shadox] would only create a drag on your final return and increase transaction costs", is simply not accurate. More about this specific point in a future post.

In the meantime, I will let this excellent example from The Sun's Financial Diary, speak for the merits of diversification. I suspect that if diversification beyond equities was not a worthwhile undertaking, a sophisticated investment team such as Yale's endowment managers wouldn't bother with it... 'nuff said.


Matthew said...

Good discussion here Shadox. Two point to discuss... I'll split the second one out to another comment.

I think the point that gives rise to our disagreement here is how we define volatility. We both agree that volatility is the relative change in price over time.

But in order to quantify the term, you and I must agree on a unit of time over which to measure. Therefore, volatility is a function of time.

Using your S&P500 example, what is the volatility of that index? If we agree to measure it over the course of a year, then I calculate a standard deviation of about 15%. If we measure it over a five year interval, it's 7%. 10 years - 5.3%. And if we measure it over thirty years, the standard deviation is only 1.5%, practically nothing.

So which number accurately describes the volatility of the S&P500? Of course they all do.

It's also worth noting that the expected return does not change over the different time periods - it's always ~7.1%.

Matthew said...

As we saw in my S&P example, as we extend our time horizon out far enough, then the volatility associated with our equity asset class converges to (almost) zero. This phenomenon follows for all other asset classes too. At that point, it would be illogical to invest in any class of asset that will deliver an inferior expected return to the leader, regardless of the volatility that may be present in a shorter time horizon.

As it stands, no asset class has outperformed equities over the 50 year time period. So I stand by my assertion that one should be invested in 100% equities if one's time horizon is sufficiently long.

As far as your appeal to authority using Yale's endowment managers, these individuals are responsible for balancing two contrary objectives: generating a cash flow to sustain the university, and to grow their endowment. Since these gentlemen must liquidate a portion of their portfolio occasionally in order to generate that cash flow, it stands to reason that the portion of their portfolio that must be sold is not subject to a 30 year time horizon, so my "100% equity" assertion does not apply.

Remember that volatility only matters when it comes time to sell.

Matthew @ Crazy Money

TFB said...

The volatility of the return percentage matters a lot less than the volatility of the end wealth itself. You can't eat the percentage number. The actual dollar amount is what counts. A +/- 1.5% per year compounded over a long period of time can be night and day in terms of end wealth. The longer the time horizon, the greater the variation. Please refer to this excellent (long) article by John Norstad on this topic. Just scroll down to the bottom and look at the chart.

Shadox said...


Your argument is a good one, to a point. There are four problems I can immediately see with that argument:

1. You assume that the past will be the same as the future. It MAY be that stocks generated the highest yield historically, but you know what they say: past performance is no guarantee of future returns...

2. You assume that you always know your time horizon. In reality, that is not an easy thing to know. You think you are saving for retirement, but what if you need the money earlier? e.g. medical emergency.

3. You assume that diversification lowers your return. That might not be the case. If you diversify inot an uncorrelated asset class with similar returns, your expected return will not suffer. In a coming post this week, for example, I discuss commodities as a potential asset class of interest. Real estate (REITs) also generate a high return while offering significant diversification benefits.

4. Re-balancing - given multiple asset classes that have an expected annual return, and tend to regress to that mean, if a certain asset class out-performs in a given year, re-balancing will tend to lock in those gains. Thus, a portfolio made up of several asset classes with more or less the same returns can be expected to yield a higher return that any of the asset classes on its own, if automatic re-balancing is performed on a regular basis.

Bottom line: even if your short term risk is completely irrelevant to you, asset class diversification is a good idea.