I will try to use as little math and jargon as possible…
Beta is one way to look at a stock’s behavior relative to the rest of the stock market. The most common way to compute beta for a stock is to compare its price over a 3 year period versus the S&P 500. The beta for a stock can be computed with daily, week, monthly or other data. Generally the difference in the final answer is small between these. Personally, I favor a beta based on daily closing values, but for this blog post I’ll stick with a monthly beta computation.
Lets compute beta for CSX versus SPY (an S&P500-based index EFT) using Microsoft Excel 2010:
- Go to Yahoo Finance and type in ticker symbol CSX.
- Click on “Historic Prices” and set the range from Oct 18, 2007 to Oct 18, 2010. Select the “Monthly” radio button.
- Scroll to the bottom of the page and click “Download to Spreadsheet.”
- When prompted select “Open With -> Microsoft Excel”.
- Cut and paste the data in the “Adj Close” column to a new spreadsheet.
- Repeat the above process for SPY. Put the SPY data in a column adjacent to the adjusted CSX closing price data.
- Compute the variance of SPY for example SPY data points e.g. “=VAR.S(C4:C40)”
- Compute the covariance of CSX with respect to SPY e.g. “=COVARIANCE.S(B4:B40,C4:C40)”
- Beta is, by definition, the value in step 8 divided by the value in step 7. However I have found this not the case when using the MS Excel 2010 formulas above. The next steps tell how I “fix” this beta.
- Compute average values for CSX and SPY: e.g “=AVERAGE(B4:B40)” and “=AVERAGE(C4:C40)”
- The fixed value is the result of step 9 * the SPY average/the CSX average. This is CSX’s 3-year, monthly beta.
Using this method, I compute a beta for CSX of 1.00. This is a fair bit different that the value of 1.24 reported by Yahoo Finance. I used the same process for MSFT and compute a beta of 0.93 versus Yahoo Finance’s 1.03 for Microsoft stock. Looking for a more out-there beta, I repeated the process for C (Citigroup). I computed a beta of 4.39 versus Yahoo Finance’s 2.65. For another comparison Google Finance reports betas for CSX, MSFT, C of 1.2, 1.05, and 2.54. Finally, MSN Money reports betas of 1.21 ,1.06, and 2.55.
It irks me that 1) these 3 finance sites don’t detail their beta-computation methods, 2) They produce different results, 3) My method produces different results, 4) MS Excel doesn’t [I don't believe] offer a beta or beta.finance function, 5) I have to tweak MS Excel data to get a more reasonable beta computation.
Be that as it may, I managed to explain one way of computing beta, and did so with a minimum of math. Please feel free to flame this post and tell me a better way. Until then feel free to try my method, or create your own modified method.
P.S. — I did some web searching and found an alternate method that is pretty decent:
http://faculty.babson.edu/academic/Beta/CalculateBeta.htm
They also perform a monthly 3-year beta computation. I like that it is clear, correct, and easy to follow. I don’t like that it uses an older version of Excel and that it requires graphing and essentially reading the numbers off of the graph.
- What is the average weighted expense ratio for all my holdings?
- How much, if anything, did I pay in commissions in the last 12 months.
- What was my rate of return in the last 12 months? (post all fees and expenses)
- How does that compare to the to rate of return in the S&P 500 in the same time period. (inclusive of dividends)
- What is the 12-month standard deviation of my investment portfolio? (a measure of risk)
- What is my asset allocation between stocks, bonds, and other?
- Do any of my holdings have loads? If so why?
- How diversified are my holdings?
Bonus: Please update me on my portfolio’s tax efficiency and tax efficiency strategy.
Feel free to take good notes, and, if you like, send the answers to me. I’d be glad to give you my personal assessment/opinion.
As I sit on a packed flight from Denver to Chicago, I contemplate the micro-economic vignettes I see. From paying extra for covered parking, to getting my shoes shined by a gentleman from Chihuahua Mexico, to the extra payed for priority boarding and expedited security screening. My trip is a series of microeconomic choices.
As I was getting my shoeshine, I chatted with Miguel. I wanted to practice my broken Spanish so I asked “¿Cómo se dice? ‘Where are you from?’”. He replied “¿De dónde eres?”. After several tries I managed to repeat the question with satisfactory pronunciation. Then I asked “¿De dónde eres?” and he replied “Mexico”.
During the next couple days in Chicago I met two people on separate locations who were from Bulgaria but spoke better German that I do (I studied German for 4 years and can converse enough to feel reasonably comfortable at a German dinner table conversation). And, Chicago, being Chicago, I encountered a wide variety of people from various and sundry places around the world.
In general the primary reason they are here in the States now is economic. The economic opportunity here, even in the current abysmal economy, is better than most places in the world.
The financial literacy of folks also varied widely. I heard a comedian quip that she thought a 401K was some kind of marathon run. Many of the folks I interacted with probably were close to that end of the financial literacy spectrum. The did, however, know that they could make much better dinero in Denver or Chicago than in Chihuahua or Bulgaria.
Other folks I had longer interactions with were financial professionals of various stripes. A couple were traders focused on interest rate futures and options. I had long conversations with a financial software developer who also does extensive corn futures trading. He has seen the financial trading floor evolving over the years. The floor is a bit quieter and littered with half as many discarded bits of paper because more and more of the action is moving towards electronic trading.
Tomorrow is primary election day in Colorado. The turnout is very high, and I am happy to see that.
There are 3 finance-related issues on my mind this election cycle:
- Fiscal discipline.
- Treasurer races. How does Colorado invest for pensions?
- Taxes. How does Colorado structure its tax code? Especially sales taxes and the internet.
These are the financial investment issues on my mind. What are yours?
Call it a whim, but I’m short term bullish. I just put in a market order for 100 shares of TOT. It will execute the trade at market open tomorrow. I’m also very happy about my JNJ buy-write. It has worked nicely so far; I collected my dividend, and I’m about 50/50 to close out the option+position on Friday for a modest profit.
These are Crazy Ivan Account (CIA) trades. My “sane and steady” portfolio is much unchanged. I reallocated about 2% from equities to TIPS – a relatively big move by my standards. I also moved about $13K from equities to the newly re-opened Vanguard Convertible Securities Fund. I viewed this latter move as largely an equities to equities move. Both of these transitions are in my tax-differed accounts. My taxable accounts are largely unchanged except for certain modest real-estate-related actions.
The common theme of my recent moves is pursuit of yield. I’ve typically had a larger than typically overall cash holding in my portfolio. I’ve preferred cash yielding 3-4% to bonds yielding 4-5% simply because of the flexibility. In the same vein I’ve been pretty dogmatic about using any “spare cash” to pay down even my personal and company ~4-5% mortgage(s)/HELOC(s). But with long bonds yielding 3% and cash yielding next to 0%, I’ve had to reinvent my investing posture. Convertibles, munis, real estate, and modestly high-yield value stocks are gradually creeping into my investment mix.
Zen is uncomplicated. Investing is uncomplicated, until it isn’t.
I like the short Zen story about attention. It starts out
There’s an old Zen story: a student said to Master Ichu, ‘Please write for me something of great wisdom.’
Master Ichu picked up his brush and wrote one word: ‘Attention.’
Simple. Right?
On some level the concepts are simple. They are also profound. On some level Zen is remarkable, stunning. On another level unremarkable.
Investing concepts are similar. Simple, profound.
Possibly the most difficult investing thoughts to grasp and put into action are the most simple.
- Save.
- Balance.
- Own.
- See.
I believe these simple words capture all you need to know to be a wise investor. Like ‘attention’ these ideas benefit from lots of practice.
To ‘Save’ is easy for some, difficult for others. Investing starts with savings. For those not born into a great inheritance savings is crucial. Savings is the art of spending less than you make. The art of delayed gratification. Keeping some of your income and keeping it safe. For many the verb ‘save’ is easy in the way that the verb ‘diet’ is easy. Simple concept, challenging action.
‘Balance’ is a deceptively simple term. Martial arts train balance. Speed skating, ice skating, and tight-rope walking showcase balance. In the investing arena ‘balance’ refers to two key ideas: diversification and emotional equanimity. Diversifying means balancing risks between different types of assets. Emotional balance means “Caring about your investments, but not THAT much.”
To fully ‘own’ your investments you must understand, control, and value them. In the same way that a stable master may own and value a prize horse without understanding veterinary medicine, a stock holder may own and value a stock without being a financial comptroller. An owner cuts out the middlemen and makes decisions. An owner weighs decisions and responsibilities carefully because the financial buck stops with her and no one else.
Finally, to ‘see’ your investments you must see beneath the surface. You see that all investments inevitably change. You see that some good investments go bad. You see the fog that shrouds some investments so thickly that you move on by. You see that taxes are constantly changing and possibly that an accountant may see the ever-changing tax waters more clearly than you.
That’s it. To invest with wisdom is to save, balance, own, and see.
Now for a curve ball. If you have been shot by poison arrows, first carefully remove them. Do not dwell on the cause of their intrusion into your flesh. After you have recovered, you may be tempted to ask “Why was I shot?”. It is the ‘why’ that takes most of the ‘attention’. The same is true for investing. The ‘why’ is the tricky, time-consuming, complicated part.
I believe that for the beginning investor the why can be unimportant. For the enlightened investor the why is also unimportant. The journey to investing enlightenment is about discovering the why and then letting it go.
I’ve now got a spreadsheet where I can enter 3-year daily stock price data and get a beta versus the S&P500 as modeled by the ETF SPY. There are still a few finer points I don’t like about the modeling. The biggest remaining gap in the computation is that the model doesn’t account for dividends on either the stock or the S&P. Ideally it would add the dividend into the price on the ex dividend date. If I could find a source where that data is built in or I took the time to merge the data it I would be set… but I haven’t bothered to do so. Another nice feature would be an R-squared computation.
So now what? Probably nothing for a while. I’m already thinking about different things. Most are things I wish other people would do 
.
- Create a low expense-ratio ETF that tracks a passive covered-call index like BXM. (No, and not an ETN… I want collateral!)
- Create an open-source format for storing and sharing stock, index, portfolio, bond, ETF data. Perhaps XML-based. Nice features would be handling of splits, ticker symbol changes, dividend and ex-dividend dates, and market holidays. Support for different time periods would be a must. Support for earnings, book values, revenue and other supporting data would be nice. Perhaps such a format already exists?
- Glue together this format with cool graphing software like Open Flash Charts and/or something HTML5 based.
- Open source statistical tools to work with this format to compute volatility, beta, R-squared, P/E ratios, etc.
Until next time, happy financial modeling.
I’ve crunched my first set of numbers. Specifically I’ve computed the beta of XOM (Exxon Mobil) vs. SPY (SPDR S&P 500 ETF) for 365 days ending Feb 4, 2010. My computed beta is 0.125. This is based on daily sampling of closing prices for a 365-day period. Not content with non-uniform sampling (e.g. discarding holiday and weekend data when the markets are not open), I recomputed beta over the same period with interpolated weekend/holiday data and came up with a beta of 0.117. I have not yet bothered to compute R-squared.
These are surprisingly low betas. Also interesting is the difference data interpolation can make… a not insignificant difference of 8.6%
Next I checked out reported betas from other sources. Yahoo Finance reports a beta of 0.35 for XOM (without specifying a time period, sampling method/frequency, or even reference index). MSN Money reports a beta of 0.43. This is a difference of about 23%. This could probably be accounted for by different time periods, etc. But what is most annoying is that these betas are presented without any such context.
I’ve only just started to explore this topic, but I think I’ve started to show that there is significant room for improvement in computing beta. And because beta underlies CAPM and modern portfolio theory, I think this is a big deal.
I’ve already got some more ideas for part III of this series, I just have to crunch some more numbers.
I’ve been blogging a lot recently to the lay investing community. I feel it is time to geek out a bit and exercise my inner quant (Quantitative analyst). I was in the shower thinking about beta and expected return. My mind came back to something that has bothered me for years… that beta is not rigorously defined. It occurred to me, strikingly, that if beta is poorly defined then so is alpha!
Now this is somewhat unsettling since CAPM is highly wedded to the concept of beta, and alpha [which some scholars believe is approximately 0]. Let me be clear, the sampling frequency and sampling period of beta are not consistently defined! One common definition of beta is based on monthly sampling over a period of one year. Another definition I’ve seen is monthly sampling over a three year period. I’ve also seen daily (trading days) sampling over periods of about 1-3 years. Investments 6th Edition (Bodie, Kane, and Marcus) even mentions the Merrill Lynch concept of adjusted beta (= 2/3 sample beta + 1/3).
These fast and loose definitions of beta are in sharp [no pun intended] contrast to the more rigorous definitions of maturity, duration, coupon rate, yield to maturity, etc. in the study of bonds.
The net effect of “beta sloppiness” is that a given given security, on the same day can get different betas from different investing houses even though they are all using the same data! To put it mildly, I think this is kind of a big deal. Beta, alpha, efficient frontiers, “risk free assets”, and CAPM are all interesting and useful concepts. I think that after 50+ years, it is finally time to put a bit more rigor into the fundamental building blocks of modern portfolio theory. I plan to crunch a few numbers and refine and test a few ideas, and I intent to help start doing just that (or at least help encourage others to) in the weeks ahead.
Just a quick note to…
Get this idea out into the blogosphere before someone tries to patent it:
Flex-flow deposits that automatically (and dynamically) re-balance a portfolio. A target asset allocation is set. Weekly/monthly inflows are initially proportioned account to these ratios. As time goes on and investments go up and down the inflows are adjusted to help keep to asset allocation close to target. More $ are invested in under-weighted funds (below tgt funds) and less $ are invested in funds that are over asset allocation targets.
There are lots of neat mathematical/algorithmic implementations. The simplest contributes to the most under-weighted fund 100% or whatever amount is need to bring into balance. Then the next most out-of-balance fund… etc. Another strategy is to perform a linear delta-weighted scaling factor. Another means is any number of non-linear delta-weighted scalings. In any case a unit-sum “percentage” vector (M-dimensional , where M is the number of funds in the target).
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