WhereDoesAllMyMoneyGo.com» DFA

Market Rally: Proceeds of Tax Loss Selling?

Preet — Wed, 07 Jan 2009 02:36:16 +0000

You have to wonder with December 24th being the last day to sell Canadian stocks in order to be able to claim a capital loss for the 2008 tax year if the current multi-day winning streak is a true turning point, purely anomalous or perhaps the result of the proceeds of a lot of tax loss selling.

What Is Tax Loss Selling?

In a nutshell, if you sell a security that is trading at a loss from when you first purchased it you can sell it to realize the loss. You can carry forward this loss and apply it against future capital gains – net result is that you can reduce your tax bill by doing this. This all assumes we are talking about non-registered accounts. One further caveat is that you cannot just purchase the same security you sold the very next day – you have to either buy something different or wait 31 days to buy back the security you sold in order to be eligible to claim the loss. Further, in order to qualify for a certain calendar year your trade has to settle before the end of the year – that meant that December 24th was the last day to sell any securities at a loss and have it qualify for the 2008 tax year (since there were only three trading days after that, and trades take three days to settle!). For a more detailed explanation of tax loss selling, please read this article on the Million Dollar Journey.

Is It Just Money Looking For a Home?

With 2008 being such a dismal year, many people had planned on doing some tax loss selling (or tax loss harvesting as it’s also referred to). For those people, they may have planned on waiting to re-deploy their cash proceeds until the day after the last day for tax loss sales eligible for 2008 to take place, since in theory people would be selling right up until that point (the ones selling for tax purposes anyways). Selling pressure = more price declines so it makes sense to wait to buy until you think the selling pressure has subsided. Given that there is potentially a lot of money sitting on the sidelines, this shoot from the hip theory isn’t all that far fetched. Take a look at the chart to see the recent market action.

It’s worth noting that the price of oil has been on a tear as well, and since the TSX is so heavily swayed by the price of oil perhaps the timing of the last day for tax loss selling is just trivial. In either case, it’s worth noting that volume hasn’t been anything to write home about during this brief rally – which from a technical perspective indicates caution is warranted that this rally may be short lived.

What’s that? Forget trying to figure it out and just buy an index?

…bah! You’re singing to the choir.

Dimensional Fund Advisors Part XIII

Preet — Tue, 07 Oct 2008 01:58:00 +0000

This article is one in a long series which I hope will help explain the ins and outs of DFA – Dimensional Fund Advisors. NOTE: This is my interpretation and explanation only. For the final word, please refer to the DFA Canada Website. To read other parts in this series, please CLICK HERE for a listing of all articles.

Picking The Right Benchmarks

For Canadian equity fund managers, beating the TSX Composite Total Return Index is a big deal. Not many managers can do it for long periods of time and those that do are celebrated with the holy label of “adding alpha”. The same can be said of US Equity Fund managers, International Equity Fund managers, et cetera with respect to their traditional benchmark indices. The problem is that the practice of comparing an equity fund manager’s performance using a CAPM world is that you assume that returns are simply a matter of exposure to the market factor (Rm – Rf). Given what we’ve learned about the dimensions of returns, namely that there are three factors (market factor, size factor and value factor) and not one factor that determines returns, ajudicating alpha based on exposure to only one factor seems a bit outdated. Yet this is how the industry operates. Why we are comfortable drawing on science and academic research from decades ago (CAPM) but have yet to adopt newer research (Three Factor or even other models that do a better job of explaining the variations in portfolio returns) is a bit puzzling… until you realize how much money is earned in an industry in which CAPM alpha falsely identifies value more readily.

Measuring Alpha In A Three Factor World

Things don’t look so rosy once we start recognizing that the performance expectations change when we examine the Size and Value loadings a manager’s portfolio takes. So for example, if a fund tilts towards smaller cap stocks than the index it is expected that the long term returns will be higher. Likewise, if a manager tilts towards value stocks (as measured by higher Book-to-Market ratios than the index) then again a long term increase in performance is expected.

Let’s take a look at this graphically. The following graph has quite a bit of information to digest, but we’ll tackle it bit by bit:

(Click to enlarge)

The first thing to notice is that we’re looking at two dimensions of the market and not three. We are assuming that we are dealing with an all equity portfolio and we can measure the size and value loadings on this graph. The total stock market is represented by the point at the cross-hairs. A portfolio can tilt towards Value or Growth, and towards Small Cap or Large Cap versus the total market portfolio (which is all stocks in the market together on a cap-weighted basis). You’ll also notice that the S&P 500 index is plotted on the graph and it is NOT the same as the total market portfolio. This is because the S&P 500 tilts towards Large Cap. Considering that the total market consists of thousands of stocks and the S&P 500 only consists of about 500 of the largest stocks on a cap-weighted basis it only makes sense for the S&P 500 to tilt towards Large.

Taking Loadings Into Account Changes Performance Expectations

The second thing to notice is the “sample fund” data point in blue. This sample fund tilts towards Small Cap stocks and as a result it’s return is expected to be quite higher than the total market over time. With a higher expected performance in the Three Factor world, alpha which appeared in a CAPM world may not exist. As I alluded to in Part II of this series, the Fidelity Magellan fund when helmed by Peter Lynch provided both CAPM alpha and Three Factor alpha, but post-Lynch it provided negative Three Factor alpha even though it beat the S&P 500. This is because once you take into account the Size and Value loadings of Magellan you’ll see that it’s performance was expected to be higher than the S&P 500, but the post-Lynch performance was somewhere between the performance of the S&P 500 and the expected performance – which muddies up the optics for most investors and advisors who are used to a CAPM world.

Next Time

Okay, I’m going to start getting into what I think is the true differentiator of DFA versus all other index funds – the engineered trading. Any “manager-less” portfolio normally has a mandate to reduce tracking error – DFA rejects this as a costly and potentially foolish objective. So if you’ve ever wondered why a DFA fund has a large tracking error when comparing it to a seemingly similar benchmark there is a method to their madness! …stay tuned.

Dimensional Fund Advisors Part XII

Preet — Tue, 23 Sep 2008 01:51:45 +0000

How Accepted Is The Three Factor Model?

The acceptance of the Three Factor Model is probably more widespread than people realize. While most investors have probably heard of the Capital Asset Pricing Model (CAPM), most have not heard of the Fama-French Three Factor Model. In fact, of all the textbooks I’ve had to study to become a financial advisor or attain new designations they all seem to have a refresher section on CAPM – but no mention of the Fama-French Three Factor Model (FFTFM).

So why then, would I say that the FFTFM is more widespread than people realize? One need only look at the following style box which might be very familiar:

These types of style boxes became popular in the mid 1990’s and have been used ever since to characterize the holdings of mutual funds and other portfolios. For the most part, investors and advisors learned to compare “like with like” – such that if you had a portfolio or fund that fell into the Large-Value box, then the straight performance comparison to a Small-Growth fund was considered an apples-to-oranges comparison (and not an apples-to-apples comparison). Today, everybody just “knows” that such a comparison isn’t fair.

If the only major determinant of portfolio performance was exposure to equities (as according to CAPM), then looking at these style boxes shouldn’t really give you any more information. That investors and advisors DO look at the fund’s size and value characteristics is a testament to the FFTFM and that the other major factors in determining portfolio peformance could indeed be Size and Value (and not just exposure to the market in general).

The Lipper Indices

The Lipper Database also converted to a multi-factor framework in 1999. Here are the Equity Indices as of March 9th, 1998:

Capital Appreciation
Growth Fund
Small Cap Fund
Growth & Income
Equity Income Fund
Science & Tech Fund
International Fund
Gold Fund
Balanced Fund
Emerging Markets

Here were the Equity Indices as of November 20th, 2000:

Large-Cap Growth
Large-Cap Core
Large-Cap Value
Multi-Cap Growth
Multi-Cap Core
Multi-Cap Value
Mid-Cap Growth
Mid-Cap Core
Mid-Cap Value
Small-Cap Growth
Small-Cap Core
Small-Cap Value
Equity Income Fund
Science & Tech Fund
Gold Fund
International Fund
Emerging Markets
Balanced

To Be Continued…

Well that’s all fine and dandy, but where this is really going to start getting interesting is when we start using a Three-Factor analysis instead of CAPM to measure mutual fund manager performance. I’ll spoil a bit of the surprise when I say that CAPM alpha does not usually translate into Multi-Factor alpha which isn’t good news for the few managers who have beaten their benchmarks. Stay tuned!

CLICK TO HERE TO GO TO PART XIII

Dimensional Fund Advisors Part XI

Preet — Thu, 11 Sep 2008 04:03:42 +0000

Criticisms of The Initial Findings

As noted at the end of Part X, there were some early criticisms of the Three Factor model after the publication of the paper The Cross-Section of Expected Stock Returns in 1992. (As an aside, I understand that this paper has been the most cited finance paper in the last 20 years.)

One of the main criticisms has been that Fama and French were simply data-mining. After all, the paper had only looked at the period from 1963 to 1990 and only at the US stock market. Some argued that with all the academics sifting through the reams of data on the markets it’s only natural for someone to find some patterns that work really well, but have no real explanation other than ‘it was observed’.

To address the short sample size, when the data was available going back to 1927 the same analysis was done and the results even more robust. (I don’t have the R² numbers for the 5×5 matrix of the market for the Three Factor model on hand, but here are the summary statistics for the annual returns for the market and different sections of the market.) I have included this data which was provided by Eugene Fama and DFA (ditto goes for all other data in this part). The original data from 1963 to 1990 was extended to 2007, and 1927 to 1962 was analyzed separately and then finally all the data from 1927 to 2007 was looked at as well:

For those who are interested, here are the numbers in table form, which you can click to enlarge:

One thing to note is that Small Growth seems to have anamolous results with respect to the standard deviation numbers. It would seem that investors in small growth stocks do not get as fairly compensated for the risk they are exposed to compared to other sections of the market.

But What About Different Markets Altogether?

Okay, so we’ve seen some data from an earlier time period and the results were basically in line with the theory, and of course looking at both the original time period and earlier time period and then adding on the data for recent history also showed that there seems to be size and value premia.

…at least for the US market. But what about other markets?

According to William Bernstein, “Value and size premia were found on every hill and under every rock.” You can read his full article which commemorated the 10th anniversary of the now famous Fama French paper by clicking here. Note that he also provides some hints as to how a non-DFA investor might take advantage of these premia, which I will also address later in this series. But for those who are satisfied to stay here and look at more charts, next up is some data for the MSCI EAFE index:

Followed next by some data on Emerging Markets:

And finally, here are the observed value premia for 13 individual equity markets from 1975 to 1995.

A value premium shows up in 12 of the 13 markets with the exception of Italy. I will add that in 1975 there were only 72 companies in the Italian equity market sample and it had an annual standand deviation of 43.77 during this time. (Many of the other markets had few companies in their public markets as well, and the reasons for not seeing a value premium in Italy could also explain why we see a value premium in those other markets to be fair: the time and size of those market samples are relatively small.)

Okay, I think I’ve bombarded you with enough charts for one sitting. Hopefully this isn’t getting too boring. In Part XII we will look at how the Three Factor Model has crept into the world of retail financial services and this will be a bit more interesting.

CLICK HERE TO GO TO PART XII

Dimensional Fund Advisors Part X

Preet — Tue, 09 Sep 2008 02:59:10 +0000

Introduction To The Fama-French Three Factor Model

First, as a refresher let’s look at the CAPM. Remember, this asset pricing model (the “single” factor model) says that an investor’s expected return is based on their exposure to the market factor (or Beta). Here is the formula again:

E(Rp) = Rf + β(Rm – Rf)

As I alluded to in the last part of this series, the Fama-French Three Factor Model (FFTFM henceforth) uses three factors to explain expected return: 1) Market Factor, 2) Size Factor, and 3) Value Factor. Just as CAPM includes a measure of the amount of exposure to the market factor, the FFTFM includes measures of the exposure to each of the three factors.

The Fama-French Three Factor Model:

E(Rp) = Rf + β(Rm – Rf) + s(Small – Big) + h(High BtM – Low BtM)

(Small – Big) and (High BtM – Low BtM) are analogous to (Rm – Rf). Remember that (Rm – Rf) is the equity premium or market factor – it is just the excess return of stocks over t-bills. Similarly (Small – Big) is the excess return of Small stocks versus Big stocks, and (High BtM – Low BtM) is the excess return of Value stocks over Growth stocks. You can think of each as having their own Beta, except it’s not called Beta for each – it’s only called Beta for measuring the sensitivity to the market factor. There is not really a name for the “other” Betas, they are just represented as “s” and “h” – each is just a measure of the amount of exposure to the other two factors (size and value).

In fact, the way the formula is normally written uses SMB to represent “Small Minus Big” and HML to represent “High BtM Minus Low BtM”. Therefore you will see the formula written as follows (but it means the same as above):

E(Rp) = Rf + β(Rm – Rf) + s(SMB) + h(HML)

And, just to bash you over the head again with the same old thing, in plain english this is saying that the investor’s expected return is equal to the risk-free rate PLUS their exposure to the market factor PLUS their exposure to the size factor PLUS their exposure to the value factor.

Okay Preet, So What?

Well I suppose the best way to explain why this three factor model has garnered so much attention is to look at how Fama and French looked at it. They took the total stock market and they chopped it up into a 5 x 5 matrix (Book to Market quintiles by Size quintiles) as follows:

It is also important to know what R² is – according to Wikipedia: “the coefficient of determination, R², is the proportion of variability in a data set that is accounted for by a statistical model… R² is a statistic that will give some information about the goodness of fit of a model. In regression, the R² coefficient of determination is a statistical measure of how well the regression line approximates the real data points. An R² of 1.0 indicates that the regression line perfectly fits the data.” Basically the closer to 1.0 the R² is, the more “explanatory power” of a model.

If you look at the CAPM regressions for “monthly value-weight portfolio returns from July 1963 to December 2007″ for a total of 534 months of data (information sourced from Eugene Fama and DFA) then the R² values for this 5×5 cross-section of the total market looks as follows (remember, this is for the CAPM):

So what is being said here is that for each slice of the 25 slices of the market based on differing size and value factors, the CAPM really only does a half decent job for larger stocks with low Book to Market values – coincidentally, the S&P 500 has many large cap growth stocks. But once we stray away from this, the CAPM does an increasingly poorer job of explaining the variation in returns. Of course, this begs the question: what about the Three Factor regressions? I have to admit, my life changed a bit when I saw the next slide.

Here are the “Three Factor Regressions for Monthly Value-Weight Portfolio Returns from July 1963 to December 2007″, again a total of 534 months of data and this was sourced from Eugene Fama and DFA, and again looking at the R² values:

I’ll stop there for today, but Part XI will address some of the early criticisms of this model. Part XII will look at how widespread this model has become, even though you many not realize it.

CLICK HERE TO GO TO PART XI

Dimensional Fund Advisors Part IX

Preet — Thu, 04 Sep 2008 02:37:47 +0000

Risk and Return Revisited

If we are looking at the long term numbers of a diversified portfolio of value stocks outperforming growth stocks, and small cap outperforming large cap, then we should see increased risk in the form of increased standard deviation if risk and return are truly related. After all, one of the main beliefs of DFA is that “markets work” and risk and return are related – so if there is more return to be had, it MUST come with additional risk.

Here are the return numbers presented again, but this time with the standard deviation numbers added as well:

You can see that the Value stocks and the Small stocks carry much higher standard deviations to go along with their higher annualized returns. The data showing Value stocks having higher returns and higher risk than Growth stocks may be against the conventional wisdom – most people assume growth stocks are riskier, but the long term data shows otherwise.

Let’s Take Another Step…

Now, let’s take a look at the Value effect WITHIN Large Cap stocks and WITHIN Small Cap Stocks. In other words, we are going to see if Large Cap Value outperforms Large Cap Growth, and we are going to see if Small Cap Value outperforms Small Cap Growth – and again we will toss in the standard deviations to serve as the main proxy for risk.

Data and Chart sourced from DFA Canada

Compounded Returns versus Average Return

First thing to note is that you actually see two sets of returns for each item we are looking at. It is important to note the distinction as pointed out by Michael James on Money in a comment in the last part in the series. The “Annualized Compound Return” is more meaningful since it allows you to figure out what your experience would’ve been if you had (and could have) actually invested in these indices (we’re not taking into account transaction costs, or the fact that you couldn’t really invest in anything that could track these indices since their inception). The “Annual Average Return” is simply taking all the annual returns and dividing by the number of years to get the average return you would expect for any year. (You can visit Michael James’ blog by clicking here)

More Support…

Nonetheless, we see that for Large Cap stocks, there is again a Value premium in that Large Cap Value outperformed Large Cap Growth. We also see that within Small cap stocks the Value premium still shows up in that Small Cap Value outperformed Small Cap Growth. (However, we do also notice that the standard deviation on Small Cap Growth is not as low as we would expect relative to Small Cap Value. This indeed one of the very few anomalies with the Fama-French Three Factor Model [which I have yet to explain in detail!] since the data implies that the risk and return relationship in the value premium does not really show up for Small Cap stocks. This is acknowledged by Fama and French.)

I’ll end there since we’ve again covered a lot of ground. In Part X, we will finally see the Fama-French Three Factor Model formula and then start comparing this to the Capital Asset Pricing Model.

CLICK HERE TO GO TO PART X

Dimensional Fund Advisors Part VIII

Preet — Thu, 28 Aug 2008 04:27:31 +0000

The Problem With CAPM

A quote taken from a piece written by Eugene F. Fama, Jr (son of the researcher Dr. Eugene Fama, Sr):

“The single-factor model (CAPM) is grounded in an elegant theory. The rationale is sensible. It’s a great model in every respect except for the fact that it doesn’t work. It did a decent job when the world of investments was mostly managed versions of the market, but the further the portfolios got from the market, the less the model explained their returns.”

What is being said here is that CAPM does a poor job explaining the variability in returns when a portfolio is too different from the broad market. I think the best way to explain this is with hard data.

Dissecting The Market

First of all, we need to be clear that the data is regarding the US stock markets in US dollars. We’ll discuss other markets (i.e. Canada) in due course. Fama and French looked at many ways to dissect the market in order to find other factors that lead to higher returns – two factors they identified were Size and Value, but let’s see why they think these are additional factors over and above the market factor.

The Size Factor

The chart below is the US stock market which consists of all stocks in the NYSE, NASDAQ and AMEX except for ADRs, closed-end funds and tracking stocks from July 1926 to December 2006. The ‘market’ portfolio is all stocks that fit this criteria. The ‘large’ portfolio is composed of stocks with market caps in the top 30% of NYSE market cap. The ’small’ portfolio is composed of stocks with market caps in the bottom 30% of NYSE market cap. The performance shown is the annualized average of the monthly rates of return and is originally sourced from Fama & French’s research.

You’ll note that Small cap stocks outperformed Large cap stocks quite handily. The difference in this case is an annualized average of 4.69% and is a statistically significant result (i.e. not due to chance according to the data).

The Book-to-Market Factor (Value Factor)

I suppose I should avoid calling this the “value” factor where possible since calling it that is a bit of a misnomer. For the most part, investors today relate “value” as stocks that are temporarily mis-priced by the market and you’ll see that the data does not actually support such a notion. This is one of the areas which will seem to contradict conventional wisdom (i.e. that value stocks are less risky than growth stocks).

First we need to define Book-to-market. This is simply the Book Value of a stock versus the Market Value of a stock. Book value is like the accountant’s estimate of the value of a company based on assets minus liabilities and market value is just the overall market capitalization as determined by the stock price. So if a stock is trading at a low price, than the ratio of Book value to Market value is higher – and this indicates a “value” stock. If a stock is trading at a higher price, than the ratio of Book value to Market value is lower – this indicates more of a “growth” stock. For the purposes of explanation, I will use value and high book to market interchangeably, and growth and low book to market interchangeably.

The chart below shows the annualized average rates of return for the market versus ‘value’ (or ‘high book to market’) stocks and ‘growth’ (or ‘low book to market’) stocks, again based on monthly rates of return from July 1926 to December 2006. Value stocks are identified as stocks with positive BtM’s in the top 30% of NYSE BtM distributions and Growth stocks are identified as stocks with positive BtM’s in the bottom 30% of NYSE BtM distributions.

This time we see that Value stocks handily outperformed growth stocks by an annualized average of 4.79%, which is again reliably different from zero (i.e. not due to chance).

To Be Continued…

We’re not done yet. While we have looked at 80 years of data to see that small stocks outperform large stocks and value outperforms growth, there is more data to sift through before we look at the model that Fama and French proposed that is now known as the Fama-French Three Factor Model, which has significantly more explanatory power than CAPM. You’ll remember that CAPM was a one factor model (it looked at exposure to the market factor). The FFTFM (Fama French Three Factor Model) essentially looks at exposure to the market factor, exposure to the size factor and exposure to the value factor – hence the name.

CLICK HERE TO GO TO PART IX

Dimensional Fund Advisors Part VII

Preet — Tue, 26 Aug 2008 00:02:06 +0000

Continuing from Part VI, where we saw the formula for CAPM (the Capital Asset Pricing Model), we found that the model suggests that, given a diversified portfolio, your sensitivity (β, or “beta”) to the market factor (also known as the “equity factor”) should explain your expected return.

As a refresher, here is the formula:

E(Rp) = Rf + β(Rm – Rf)

Let’s look at a hypothetical 10 year period where the risk free rate was 3%, the market returned 10% and a mutual fund manager we selected to run our portfolio earned 15% on our portfolio. The portfolio was 1.5 times as volatile as the market. According to CAPM, we can calculate what performance we should have expected, given the level of sensitivity to the market:

E(Rp) = 3% + 1.5(10% – 3%)

E(Rp) = 3% + 1.5(7%)

E(Rp) = 3% + 10.5%

E(Rp) = 13.5%

So we see that CAPM says that we should have expected an annualized return of 13.5%. BUT – you’ll note that I indicated that the manager returned 15%. (N.B.: returns are assumed to be after fees.) So in other words, the expected return (Rp) was less than the actual return. This is where Alpha comes in….

Alpha

Alpha is represented by the symbol “α”. If you go by some standard definitions, α represents the excess return of a manager over and above that which is expected by a benchmark or predicted return of a model. Calculating α is very simple. In the example above it’s 1.5%, which is calculated by taking the actual return (15%) and subtracting the return of the benchmark (which in our case is the return predicted by the model to account for the fact that the portfolio is 1.5 times as volatile as the market) which is 13.5%. This is where we get 1.5%. Note that it is possible to have negative alpha (in fact that seems to be the norm) – this indicates that the manager is underperforming what is expected, after having taking into account the risk adjusted return of the portfolio. To put it into a formula, the actual return of the portfolio (Rp) (and not E(Rp) which is the expected return) is as follows:

Rp = Rf + β(Rm – Rf) + α

I’m going to write it again and highlight a few terms:

Rp = Rf + β(Rm – Rf) + α

What I’ve highlighted is E(Rp), the expected return and is simply the CAPM formula from the top of this post. If we simply substitute E(Rp) into the above formula we get:

Rp = E(Rp) + α

Which is basically saying that the return on the portfolio equals the expected return plus alpha. If we re-arrange the terms to bring E(Rp) to the left hand side we get:

Rp – E(Rp) = α

Which is exactly what we defined alpha above when we said alpha “is calculated by taking the actual return and subtracting the return of the benchmark or expected return predicted by the model”.

Prevalence of CAPM

CAPM is very prevalent. If you go to morningstar, globefund, etc. you will see Beta numbers (usually 3 year Beta numbers) for every fund. Alpha is harder to find (my guess is because it’s usually negative). And when you do see a fund with positive alpha, it gets trumpeted by advisors (or by wholesalers to advisors) endlessly. Positive alpha is a good thing and is supposed to measure the excess return earned on a portfolio over and above what is predicted by CAPM.

Now that you are up to speed on CAPM, I regret to inform you that it has been all but invalidated. However, it is still used extensively in the retail financial services (and even institutionally) and is still taught in MBA schools.

Part VIII will begin to look at some data that is behind part of the research and theories behind DFA (Dimensional Fund Advisors).

CLICK HERE TO GO TO PART VIII

Dimensional Fund Advisors Part VI

Preet — Thu, 21 Aug 2008 00:15:51 +0000

The Capital Asset Pricing Model (CAPM)

As I mentioned before, this series on DFA is going to be long if you really want to understand what they are about. Further, there is some background knowledge that is required before we can truly make sense of what is going on. At the same time, I don’t want to go too far down some tangents so I am going to provide the coles notes on many topics.

To that end I thought it would be best to have a refresher on CAPM. CAPM stands for Capital Asset Pricing Model and the acronym is pronounced “Cap-ehm”. Basically CAPM is model that predicts what your expected return should be in your portfolio based on a few factors (actually just one factor). First let’s begin with some logic…

The “risk free” rate is equivalent to the T-bill rate (or the high interest savings account rate, if you prefer). This is basically the rate of return you can get on a portfolio without taking any risk. If you were to subject your portfolio to any risk, then you would expect to be compensated in the form of extra return, over and above the risk free rate. But the question then arises: how much extra return should you expect for each unit of risk? CAPM basically says that the expected return you get should be based on how much exposure you have to the market factor plus the risk free rate.

The “market factor” is also known as “the equity premium” or the extra return of stocks over the risk-free rate. So, to re-iterate, CAPM is saying that your exposure to the market factor explains your expected return on your portfolio.

The Formula

Here is the CAPM formula:

E(Rp) = Rf + β(Rm – Rf)

Where:

E(Rp) = Expected return on the portfolio
Rf = The Risk Free Rate
β = Beta (Which is the measure of exposure to the market factor)
Rm = Return of the Market

Note: the term in brackets, (Rm – Rf), is “the market factor” (or “equity premium”)

Before we use some test numbers to see how this works, lets first put on our thinking hats. Let’s assume we are investing using an index tracking fund (like an ETF). Since our portfolio will move in tandem with the market, we have a β of 1. Let’s put this in the formula (and nothing else).

E(Rp) = Rf + 1(Rm – Rf)

So if we multiply (Rm – Rf) by 1 we will have (drum roll please)… (Rm – Rf). So this makes the equation as follows:

E(Rp) = Rf + Rm – Rf

You can see that the Rf terms cancel each other out, leaving:

E(Rp) = Rm

Which is what we want with an index fund. We want the return to equal the market return. But now let’s plug in some numbers for a non-index portfolio and see what happens. We’ll assume that the “risk free rate” is 3% since that is what a high interest rate savings account might yield. We’ll assume our portfolio tends to move up and down one and a half times as much as the market, therefore β is equal to 1.5. The return on the market is 10%. Now we can solve to see what CAPM says our expected return should be.

E(Rp) = 3% + 1.5(10% – 3%)

E(Rp) = 3% + 1.5(7%)

E(Rp) = 3% + 10.5%

E(Rp) = 13.5%

So in this case, CAPM says that if our portfolio is 1.5 times as volatile as the market, then for it to be a worthwhile investment, our portfolio needs to earn 13.5% versus the market’s 10% in order to be fairly compensated for taking on the extra risk over the risk free rate.

I’ll stop there for today, but will continue in the next post in the series to discuss what happens when the ACTUAL return of the portfolio does not match the Expected Return.

CLICK HERE TO GO TO PART VII

Dimensional Fund Advisors Part V

Preet — Wed, 20 Aug 2008 00:00:04 +0000

A Concession

I will concede that certain investors can beat the markets, for even extended periods of time. And some investors may have tremendous outperformance (perhaps one of their original investments they made was a penny stock that is now a billion dollar company), but this is simply a reflection of the tremendous risks they may have taken. And further I will concede that there are people who exist who can flat out beat the markets (like Peter Lynch and Warren Buffett), however these people are either extremely rare or not known to the public. (Why would anyone who could beat the markets tell you about it and thereby negate their advantage?)

I believe them to be so rare that there is no point in spending time and energy in trying to identify them in advance. According to Dr. Kenneth French – 40 years of 1000’s of Ph.D.s trying to find a way to do so has proved fruitless.

An Assumption

There is one assumption that I will make that will be implied from this point forward: we are dealing with well-diversified portfolios. This is one of the free lunches in investing in that you can eliminate one type of risk that doesn’t seem to have a solid relationship to future returns: non-systematic risk.

With respect to any given securities market there exists Sytematic Risk and Non-Systematic Risk.

Systematic Risk

Systematic risk is the general ebb and flow of the market as a whole – or the tendency for all stocks to increase or decrease in value at the same time with a certain degree of positive correlation. For example, ‘Black Monday’ on October 19^th, 1987 was a Systematic event in that almost all stocks fell in value on that single day. Macro-economic events and stimuli can be expected to have broad systematic effects on capital markets – positive or negative – on an on-going basis such as interest rate levels, political events, war, etc. It is important to note that systematic risk cannot be diversified away. In other words, you could have a portfolio that is diversified with 1000 different stocks from a given market and there will always be a base level of return variance (shown as the asymptote in the figure below).

Non-Systematic Risk

Non-Systematic risk is the element of overall portfolio risk than can be largely eliminated through sufficient diversification within a particular asset class. The best way to describe it is to build an analogy. Let us assume you owned one stock – if that company went bankrupt you will have lost 100% of your portfolio. If you owned one hundred stocks, and one company went bankrupt you would have lost 1% of your portfolio. Conversely, what if that one company doubled in value? You either doubled your money or only gained 1% if you held 1 stock or 100, respectively. Non-Systematic risk is the individual business risk associated with the underlying stock – if this company goes bankrupt – this is a non-systematic risk event and generally has very little to do with the general ebb and flow of the overall markets.

(You can click on the graph for a larger view)

It is generally debated as to how many securities one needs to hold to eliminate non-systematic risk. Research has shown that between thirty and forty securities are enough to eliminate non-systematic risk.

A rational investor would be expected to take measures to eliminate non-systematic risk from one’s portfolio by increasing the number of holdings within each distinct asset class – a task that is easily accomplished through asset class indexing products which may routinely hold hundreds of asset class constituents.

The non-systematic risk amounts to “noise” that an investor doesn’t necessarily get compensated for (the expected return for the random noise is zero), so it would make sense to get rid of this risk if possible. So to re-iterate: going forward the discussion assumes we are talking about well diversified portfolios in all cases.

The next part in this series will look at CAPM (the Capital Asset Pricing Model).

CLICK HERE TO GO TO PART VI