I have been investing in the markets for about 15 years, and have also worked in finance and gathered a lot of theoretical and practical knowledge of portfolio management. So I am comfortable saying the tools available to amateur investors provide almost nothing helpful to evaluation or decision-making.
There is an extraordinary wealth of information freely available on individual investments. And it is de rigueur for websites, and even phones now, to have a 'portfolio management' app. But what this app typically does is tell you how each individual component of your portfolio is doing today, or since you bought it, and add this up for you. It does not tell you anything at all about the two most important questions in portfolio management:
- Have I been well-compensated for the risk I'm taking?
- Am I likely to continue being well-compensated for the risk I'm taking?
Implicit in 2 is "Or if not, why not, and what should I DO about it?"
All of the charts I'm going to show are not to really talk about my portfolio in particular, except that it is the only real example I have. The point is just to say "Why can't I get these charts made for me?" And to some extent, "Do you want to buy the intellectual property behind them and develop them into a real portfolio management application yourself?"
I think I have done well the last 6 years (the time I have good records for), but maybe I 'should' have done better, or maybe I did do well but am not set up to continue. The following chart shows the investment gain only of my brokerage account (netting out any savings invested over the years), measured annually.
And looked at another way, and including my 401k:
So I am outgaining the S&P 500 almost every year (interestingly, even with 401Ks, where investment options are limited and I make almost no trades). But am I just taking more risk? (The prevalent theory of investing holds that you can on average earn whatever return you want by just taking more or less risk [understand that this average includes a significant percentage of total ruin for higher risk portfolios]).
Well, the answer is in the charts. If you regress my returns against the S&P 500, you find that I have taken more risk, but have been more than compensated for it. This chart shows the regressions (S&P returns on the X, my portfolios on the Y). The intercept for the lines on the following chart are above zero -- that's what portfolio managers are going for. (The slope of the line, indicating something about riskiness, is considered just a stylistic choice for a portfolio manager. Different funds have different goals for slope (Beta), but they all want a positive intercept (Alpha).)
Six to eight years is a long time to wait to get an answer though. And if it turned out that I had done poorly, six years of it would really weigh on my ability to achieve lifetime financial goals.
To answer either of the above big two questions is really a lot of work. I have been waiting for 15 years for yahoo! or my brokerage, or anybody, to do this for me, and nobody has. Maybe because the ideas are hard to make use of for the general populace (it takes a long time to explain, even to another quantitative person, unless they have the specific background -- as long as this article is, I am NOT going to get into much detail about portfolio theory beyond throwing out some links), and there's no profit in developing such tools for broad use. Or perhaps because there is no one right answer, because there are several different provably not-entirely-right theories about it, and because each individual has their own utility function, and so on and so on, yahoo!, google, msn, etc., all just keep it ultra-basic. Still, I would like to know, am I doing good? If so, is it luck? How can I do good in the future?
There are two aspects to this. One is a classic choosing problem (and the other is portfolio management -- which will eventually be the main point of my article here). There are hundreds of thousands of possible investments. Which ones should I take? Unless you think you know more than literally everyone else put together, you can assume that all investments are fairly priced right now and it doesn't particularly matter which ones you get. This is not something most people accept easily. But basically if an investment is 'bad,' it will already be priced low enough that it should provide a positive expected return (and more or less the same risk-adjusted return on average as anything else). If 'everyone knew' it was going down, it already would be down. And if everyone knew a good investment was going up, it would already be up, but not so up that people didn't still feel like buying it. Of course, there are bubbles, and it's foolhardy to think the market is perfectly efficient. But nobody has a proven ability to detect mispricing better than the market as a whole can. Nobody. As an amateur, I sure as hell don't. So as far as choosing, I invest in stories I understand and want to follow, so I have a distant hope of noticing when the story or the environment is about to meaningfully change. This is not quite, but sort of, the idea of Peter Lynch and Warren Buffett. But it leads to a problem -- if you invest in all the same sort of thing, you are not diversified, and you are eventually going to lose big.
So the second part of the problem becomes dominant, and it is controlling how much of which investments to hold, and which complementary investments to think about. This, I know something about. Like I said, all the theories are imperfect, and parameterizing the equations in any useful way is very difficult, but I can at least look at my portfolio through the lens of portfolio theory and see if I am doing anything outrageous.
Let's ask how did I do, first. The first simple question that free portfolio trackers cannot answer is what was my portfolio value at every day in the past. Normalizing to what it was worth on 12/31/08, here it is for every day of 2009. To do this, I started with my current portfolio and backed out each transaction to get my positions on each day, then valued them with historical quotes. This was sort of hard to do, because there are so many different types of transactions that can happen and need to be backed out. I am fortunate that all the symbols I had in my portfolio throughout the year still trade, because it is very difficult to get data for companies that went private or recapitalized under a new symbol, or went bankrupt, etc. Anyway, for this particular time period and portfolio, it was possible so here it is:
An even cooler way to look at this:
Sorry there's no legend but the bottom blue band are my AAPL holdings relative to the portfolio total each day. The gold band above that is BWX. The pink band that comes in between in October is APWR, etc., all the way to the top band, which is VWO. When there is an area below zero, I am borrowing money.
The big vertical jumps are where I transferred money in. What I'd really like to evaluate is not my market timing or cash/investment allocation, but just my investment performance. So I calculate daily investment % returns and then find the cumulative % returns from the beginning of the year to each day. This also has the benefit of counting each day equally (as the portfolio has twice as much value toward the end of the year, we could mistakenly count later returns twice as much -- but that wouldn't tell us about investment performance.) Essentially, imagine my portfolio is a mutual fund, and regardless of whether money flows in and out, I want to capture the performance.
All right, so 50% gain is good, more or less no matter what. Your brokerage may calculate this final number for you, but it's difficult to get it in any kind of context. Let's put this in context ourselves. Seeing the progression over the year is one kind of context. Another is to compare the gain vs. the volatility. The daily volatility of this portfolio is equivalent to about a 25% annual standard deviation (for an ex post Sharpe ratio of about 1.9, which is good -- the index had a return of 21% and a daily volatility that translates to 18% annual standard deviation, for a Sharpe ratio of about 1.1 or 1.2.)
Still another context is to compare gains vs. some kind of benchmark. Did I just ride the wave of the market, or did I do something beyond that?
This raises the question, what benchmark? As I am inspired mostly by CAPM, I will use a proxy for THE MARKET, everything, all assets in the world, investable and otherwise. Most people use something like the S&P500, but I think that is inadequate. Even a measure of global stocks would be inadequate. So I constructed an index that has global stocks, bonds of all types, and commodities. I didn't put in anything explicitly for real estate, although perhaps it is captured by REITs. (A special comment on bonds -- while you can just look up an ETF of "all stocks in the world," there is no such thing for bonds. I researched how much money was outstanding in US bonds, other 1st world sovereign bonds, emerging market sovereign bonds, US investment corporate bonds, US junk corporate bonds, municipal bonds, and mimicked that through a portfolio of ETFs.) The total world portfolio I used was:
worldstocks = {{"VT", 1}};
worldbonds = {{"PZA", 110}, {"SHY", 25}, {"IEF", 22}, {"TLT", 22}, {"MBB", 100}, {"LQD", 50}, {"JNK", 32}, {"AGZ", 30}, {"USY", 150}, {"PCY", 350}, {"BWX", 100}};(*no int'l corp or us asset-backed etfs*)
worldother = {{"DJP", 1}};
Then, I weighted the three asset classes by their approximate size, (0.55,0.4,0.05).
If you want to be a CAPM purist, you should just buy this portfolio.
Anyway, let's see how the index did and how my portfolio (which does include a lot of bonds and commodities in addition to stocks) did vs. the index. (Green is me, black the index)
To the naked eye, it looks like I am highly correlated to the index and maybe just basically twice as risky? Was there alpha in this portfolio last year? Turns out, yes, a lot. The best fit regression (annualizing the daily returns to show a neater equation) is:
my port return = 23% + (1.24 * index return)
There's about a 0.8 R-sq there (I have a correlation of 0.9 with the index).
An interesting picture to look at is the following. What were the returns each day for the portfolio and for the index. As you can see, the volatility went down substantially as the year progressed. The market certainly calmed down from the panic state that started the year, but I also started dialing back on the risk the last few months. You can see there are zero days I'm outside +/- 2% return in the last couple months.
Without the time series angle, a neat way of looking at this info is a box & whiskers plot.
The box shows the 25th & 75th percentile of daily returns, the line roughly in the middle of the box being the median return. The whiskers are 1.5 the range of the box, with far outliers shown individually.
So in sum, it was in fact a good year. I took somewhat more risk, especially in the early part of the year. Ironically, I was more compensated in the latter part of the year. Quarter by quarter, my cumulative return and daily risk expressed quarterly was (9, 19), (9, 12), (18, 9), (8, 8). Either I got better or luckier in the second half. Skill vs. luck is particularly hard to judge, especially in one year.
So last year was a good year. I made back 3/4 of the money I lost in 2008.
:-0
What I haven't done, but at least now am in position to do is really analyze why. Which investments did particularly well compared with their covariance to the portfolio, and compared to the benchmark. Furthermore, I could even go through the scary exercise of evaluating my trades. 1 month, 3 months, 6 months after a buy or a sell, do I give the transaction a thumbs up or thumbs down? If I just stuck with my 12/31/08 portfolio, how would I have done (putting cash inflows magically into all holdings proportionally, with no transaction costs)? I could do all that now that I have this machinery in place.
What I have done though is evaluate my current portfolio to see -- if variances and covariances go roughly like they did in the recent past -- which holdings are contributing the most to my portfolio risk. Further, if we build at least some crude model of expected return, which holdings are improving my portfolio return on risk, and which are degrading it. What, in short, should I DO?
The market expects the Sharpe ratio of the market going forward to be about 0.6. I'm going to use CAPM with my homemade index, find each holdings' Beta to that index, assume some reversion to Beta=1, take the annualized standard deviation of my index to be what it has been over the last 9 months since the market stopped spazzing out (14%), and state the expected return of each holding that way. One could use any number of ways to do this, none of which work particularly well. But at least we will get a sanity check and decide, when a holding looks bad, whether we truly believe the return will be sufficient.
Before diving in to the individual holdings, let's look at the portfolio results. If I hold what I now have, and conditions are stable, I expect to earn 9.6% above the 1% risk-free rate, with an annualized volatility of 17.1%. That gives a forward-looking Sharpe ratio of 0.56, which is close to the market's 0.6. You can't expect to do better than the market. You can happen to do better than the market, like I did last year, but it's unreasonable to expect to do so. So overall, I am pleased with this, but interested in what opportunities there may be for improvement.
So keeping in mind the above implies an 8.5% index expected return above the 1% risk-free, we can take any holding in my portfolio as an example. I have some investment in IBM. IBM's volatility is 19%, but my portfolio is only 0.59 correlated with IBM stock, so only about 11% of that volatility goes into my portfolio. Using the expected return model described above, I expect IBM to return about 7% above risk-free this year (I give it a beta of 0.83 against my index.) That means IBM has a Sharpe ratio in my portfolio of 0.62. Because that is better than my portfolio sharpe of 0.56, I should think about buying more IBM.
Once I do this for each holding, I can make the following very useful plot.
The line is my portfolio Sharpe ratio. The axes are in percent, not $. Risk Contribution means the holding's standard deviation times its correlation with my portfolio (given that my portfolio contains it). The dots below the line represent holdings for which I don't appear to expect sufficient returns compared to the risk they bring into the portfolio. I should think about whether I want to sell some portion of those. The dots above the line are the opposite, and I should consider whether I want to buy more.
The huge outlier of badness is APWR. I am indeed considering whether I should sell some. It is wildly risky, and I am not sure I believe THAT strongly in it. My judgment is clouded by some all-too-typical bullshit: 1) I have held it for less than a year so would pay a high capital gains tax on it; 2) It is currently trading way above what I paid, so I have a cushion! In principle, I should not care whether I am up or down on it, just what I expect for it in the future. And it is right now contributing fully 1/7th of my whole portfolio's risk, which is kind of crazy for someone that just did this whole exercise to explore how well diversified I was. The pie chart below is not in terms of exposure weight; it is in terms of risk contributed to the portfolio weight (% risk contribution in the plot above multiplied by the amount of it I hold.)
All right, that's more than enough. I mainly just wanted to get these plots out there so that somebody would develop some actually useful portfolio management tools for the amateur investor.
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