Wonder if someone knows why the beta of a stock is affected by the trading volume on that stock.
My guess is that higher trading volumes increase price volatility so beta should increase.
Any help appreciated. Thanks.
Harrogath,
I would be interested to know where you get that statement (or is that your hypothesis?): the beta of a stock is affected by the trading volume on that stock.
Beta and volatility is two very different concepts. But to start off, we need to agree on what “Beta” is. Let us put our finance background for a moment. When you regress variable y on x, (ie y = mx + b + e ), the slope of the graph, m, is “the rate of change”, and “e” is the error term. Applying this concept to finance, you get the CAPM (it’s a sloppy derivation, but just bear with me as an illustration to the problem). The slope, “m”, becomes the beta, and the market premium is “x”.
Now volatility relates to the “stability” of prices. You can have a high beta (ie a stock with a “beta” of 10 means that the index goes up 1% and the stock goes up 3%, so the “beta” is tie to index that you use when doing a regression), but a low price volatility. If the stock price fluctuates between up 10% and down 10% while averaging out 0% return consistently when its index has a 5% return consistently, then the beta would almost be 0 (because they are not correlated. Sorry for all those quants out there, it’s a sloppy derivation again), but the volatility is high.
On another note, in a world of rational Econs (ie. maximum utitlity, risk averse…etc. If interested, read Richard Thaler’s Misbehaving), trading volume should be non-existence because if the buyer knows the true reason of why the seller is selling, then the buyer should probably not buy. In any case, higher trading volume stablize price volatility because it allows price discovery among all market agents. Think about small-cap stock or penny stock, they are usually thinly traded, but with high beta!
Hi leocfahelper,
Thanks for your response. I’m agree with most of what you presented and already knew it from theory. However, found in the 2016 L2 curriculum that beta is affected by trading volume on stocks but no detailed explanation of why and how this is true, nor the relationship of both variables.
Made some research and found a paper that talked about the subject. It is called “Trading Volume and Beta Stability”, The Journal of Portfolio Management, Winter 1981, Vol. 7, Nro 2, pp 60-64.
Only could read the first page because needed to pay for the rest. However, this only page starts telling that beta is affected by trading volume, that beta is (unfortunately) an unstable measure of risk because it changes with the size of the sample of returns (t size in the regression model) and the cronological portion of the data.
So, I need to further investigate this. It’s a pity that the curriculum didn’t clarify better, however thanks again for your input on this.
Harrogath
Just read the synopsis of the paper. The “risk” that you mentioned (that beta is (unfortunately) an unstable measure of risk) is not the “risk” that I first think of when I see the word “risk”. But you do have a valid point. The risk that you are talking about is a measurement risk (ie how accurate is the recorded variable?) as opposed to the standard deviation of the dependent variable.
Out of curiousity, I looked up my 2014 CFAI book Reading 31, 4.1.1, the last paragraph reads:
When a share issue trades infrequently , the most recent transaction price may be stale and not reflect underlying changes in value. If beta is estimated based on, for example, a monthly data series in which missing values are filled with the most recent transaction price, the estimated beta will be too small and the required return on equity will be underestimated. There are several econometric techniques that can be used to estimate the beta of infrequently traded securities.39 A practical alternative is to base the beta estimate on the beta of a comparable security. So this is saying that low volume actaully results in low ( estimated ) beta. Is the contrary also true? Let me know what you found out.
Something to consider is signal to noise in the beta estimation…if you have a stock that trades daily, there will be more noise in the daily price and return information (i.e. more irrelevant information will cause variations that distort the true beta) than in longer-term information. If you want to take weekly information over daily, for example, you wont see the as much of the noise generated by daily trading (even for the same security). 60 daily returns versus 60 monthly returns-- which do you think has more noise?
I haven’t given much thought to trading volume necessarily increasing beta, but this is another point to consider in the difficulties associated with estimating beta.