How to Calculate Fama French 3 Factor Alpha

hey everybody this is West gray over a turnkey analyst my day job is a being a finance professor at Drexel University and today we want to learn about how to calculate alpha a lot of people ask us at turnkey analysts but I don't think a lot of people actually understand the mechanics of how to actually do it so in this lesson what we're going to do is go step by step from data process to in-state calculations within Excel explain how to actually generate and calculate alpha estimates so what we're first going to do is collect some data so as you go to French data just in Google that will pull up Ken French's website and as background Ken French is a professor at Dartmouth and he does a lot of joint work with Eugene fama over at the University of Chicago studying asset prices and what they do it's a great public services they provide provide downloadable data via their website now the data we're going to use today is on the Femina the fom of french factors themselves if you're interested in details simply click on the link and it will explain I'll also explain the remainder of this presentation but click on the link and what you'll end up with is data that looks something like this you're going to have dates this MKT minus RF which represents the return on the value 8 crisp index which is essentially an index of all NYSC NASDAQ and Amex stocks minus the risk-free rate then you have SMB which is a long short portfolio between small and big stocks which is meant to capture exposure to small sized risk and in HML which stands for high minus low and this is a long short portfolio that's meant to capture value risk where value is defined as booked to market so it's high book to market stocks minus low book to market stocks after controlling for size and then obviously the risk-free rate is the risk-free rate so we first do is we get that data and I won't bore you with the the details on it but essentially post that into a spreadsheet which is what I've done here okay so now we have our time sir monthly time series with returns on the excess market return the SMB portfolio and hmm HTML portfolio and the RF per foot okay now we need something to test we want to calculate alpha and see if these managers or different strategies can actually produce value so for convenience again going off of Ken French's website let's just look at portfolios formed on cash flow to price another way to measure value and a favorite investment strategy of a lot of value investors out there so we click on that link and we're going to get data that looks like this what we have here is what Ken trench has done he's done all the dirty work is each month he has calculated the returns for a variety of portfolios that trade on stocks that have a particular measure on cash flow to price so he breaks them down into thirds he breaks them down into quintiles right here and then what we're going to be using is the decile portfolios now what are the decimal portfolios well let's say it's the beginning of July 1951 and there's a thousand stocks on the universe what we're going to do is we're going to rank all the stocks on cash flow to price and the top 100 stocks get put in the top decile the bottom 100 stocks get put in the bottom decile and then all we do is we simply calculate the returns to those portfolios and you do it on an ongoing basis for the remaining time so what I do with that data is I also put that data into the spreadsheet and I'll make this available on our website but since we have the Dessau portfolios and their corresponding returns ok so the next thing is well how do we actually calculate some alpha well one thing to understand is the this is a equation that kind of relates it but essentially the cap in theory says that the expect return on asset should be equal to the risk-free rate everyone should the mystery rate plus beta times the excess return on the market so that this is what the quote-unquote fair rate of return is now the problem is just looking at return on the market and the beta's with respect to that don't a lot of times capture the true risk that investors taking they may be loading up on small stocks or they could be loading loading up on value stocks it's not to say that these are quote unquote risk factors but investing is all about opportunity costs so if you can get these exposures for very low cost via index funds ETFs or dimensional fund advisers explicitly slices and dices universes so you can get access these portfolios then you should at a minimum hold your active managers to a benchmark that controls for all these different sort of exposures that you can access for very cheaply because if they can't provide value above and on those beyond those exposures then they're just charging you fees for something you could do for okay so let's actually calculate some alpha how do we go about doing it well looking over here at the high cash flow the price portfolio we want to see if buying these cheap stocks has any alpha so simply what we do is we go over to this sheet and I've already done the analysis but I'll walk you through it so in this cell what we do is we need to create excess return series because as I mentioned on this equation here all stocks are in the risk-free rate so if you run a regression and this is a how it's represented in a as a linear function then we know that every stocks can automatically get risk-free and that's going to show up as intercept so in order to make sure that intercept we don't confuse that risk-free rate for alpha we need to move it over to the left hand side of the equation because then the relationship is the excess return on asset is related to beta times the market premium plus beta times size premiums so on and so forth so that's why we put things in excess return format into in order to set true alpha so that's what we've done here it's just the cat the return on the top decile cash flow portfolio - the risk-free rate which is in sell right here and then obviously matched up on time and then you just simply double click that and drag the time series down and this time series in particular goes down to the end of July 2011 and everything here is in basis points and as long as it's all comparable it's not going to affect the regression so how do we collect or actually calculate alpha well we simply need to do some analysis and do a regression so we use the data analysis toolpak which is a tool within Excel that's free um you may have to add it as an add-in if you don't know how to do that simply google it you click on regression and then we're going to regress f-302 to F 1000 22 which is our dependent variable this is the returns on this high cash flow portfolio minus the risk-free rate and we have some information on the VIX here from a friend of mine so just disregard that because I'm tired of redoing this video anyways looking down it goes all the way as we would expect and then the independent variables or the factors we want to use to control for the risk in or the potential risk in this high cash flow the price portfolio is columns B through D so we're going to control for @ for exposure to the market the excess return on the market the exposure is small cats and exposure to value which again you may not believe those are quote-unquote risk factors but at a minimum you can get those exposures cheaply via index funds and other means so you should at least control for those when you're assessing alpha so we run a regression and we get the following output let's analyze this so right here the intercept is your alpha the X variable this is the beta with respect to the market portfolio - was free rate this is the beta with respect to Simbi this is beta with respect to hmm okay let's look at the numbers we'll start from the bottom up so the coefficient are the beta with respect to value is extremely put it's positive and extremely significant and that makes sense because obviously a high cash flow to price strategy is has a value tilt I mean by definition unless so we should expect to see that and what you also notice is this training strategy also has exposure to small caps which is measured by a positive coefficient on s and B so there's certainly elements of this strategy where it tilts toward small caps and now the beta is a little bit greater than 1 which suggests that it moves a bit more with the market all out controlling for all these other factors which at a first glance may suggest this is a bit more a bit more risky and now the Alpha is 13 basis points per month so if that were the actual alpha 13 basis points times 12 months a year you know that's that's a pretty nice edge that's 1/2 percent of alpha any pension or endowment manager or active fund manager loved to have that sort of excess return now the question is is it statistically significant from zero and there for that analysis we can simply look at the T stat and the p value so what the p value is essentially saying is that the probability of seeing an observation like this based on normality and fueler assumption is about 8 percent so you know week it could have been by chance and and it certainly seems to be marginally significant so we could argue that after controlling for market size and value that high cash flow the price you know may have a little bit alpha but it's hard to say if it's any different than 0 and after fees if a manager was say trying to charge you one or two percent on this portfolio then it would definitely have no alpha after after the fees are taken into account so there you have it it's a simple strategy of high cash flow to price stocks doesn't seem to have any alpha after you control for size and you now as a stress test let's see if the if this thing has any alpha when you just use the plain Jane cap BAM analysis so here instead of using all three the fama French model three factors we just want to use one so we'll just use the market factor and we'll run that regression now in this case you get a completely different story here's your alpha and here's your beta with respect to the market factor so this is your standard cap in alpha and then here you know the beta is basically one suggesting is saying is essentially like the market however the Alpha is forty four basis points a month and highly significant the probability of seeing that based on normality assumptions is effectively zero so just by changing how you control for exposures in one case a manager can look like they have amazing alpha and in another case it can look like they have pretty much no alpha so if a manager comes at you with a strategy that's basically high catch for the price they say hey look at my alpha Schmidt you can say well you don't want to dig a little deeper and do it on fama french factors and when you do that you'll notice well you don't really have alpha all you have is exposure to size and the value factor which I can get exposure to very cheaply via index funds or any other any number of providers out there so if you're going to charge me a fee and tell me that you make this or alpha I'm going to say no you better come back to me with a better product now let's test another manager out there and I don't mean to pick on the leg mason value trust run by Bill Miller Miller but this is a typical example where you have a Val value manager who's an active manager picking stocks and they like to claim alpha um but when you actually dig into the returns and compare it against benchmarks that soak up the various risk exposures are taking what you find is they basically have no alpha so quickly if we just look at it the if you just do the brain-dead strategy of high cash flow to price which doesn't take a lot of active and you can easily setup vieng etf you know it does very well especially relative to the value trust in others maybe some transaction cost issues in here because this is a fake portfolio and this is a real one but the main point is this active manager that apparently had you know crushing a market for many years you know it doesn't really seem like they have alpha but let's actually formally test it so what I've done here is I've actually created I've created time series on excess returns on the leg Mayson value trust using their monthly returns minus the risk-free rate and we can do the same sort analysis we did previously and we're going to use different section of data here there we go from right here this one goes all the way out a little bit further um our independent factors just scrolling down the page here to make sure we control for the market exposure size exposure and eye exposure make sure the regressions are matched up and we run that now let's see what's going on here with the leg mason value trust here's their alpha here's their beta with market here's their beta with SMB here's their beta with hmm Wow so actually these guys tend to have a folk a tilt towards bigger stocks with respect to value they have certainly have a value tip tilt which would make sense if their the value trust their market beta is a little bit higher than the general market and actually have negative alpha it's not significantly different from zero but it's certainly basically zero so if you were to look at the leg mason value trust and they were saying hey we want to charge you a lot of fees you would say well why you charge those fees because you don't really add any value I can essentially replicate your portfolio and you know pay index type fees now what if we look at their returns just using the cap in well let's check it out so we come in here and now let's not control for size and their value exposure let's see what happens there so again you typically get a lot different answers depending on the model you use but we have a similar result right here here's their alpha and here's their beta with respect to the market so again no alpha with this model and now their beta is essentially about the same so the conclusion we would draw from this simple analysis is that the leg mason value trust essentially has no alpha whether you control just for market exposure or you if you were to control for market exposure size exposure and value exposure and in some sense or something to be careful about is over here when we looked at the cash flow strategy you know it had 13 basis points but it was not really significantly different from 0 maybe at the margin so that's essentially zero alpha likewise over here with the leg mason value trust sure the point estimate is negative but again it's probably not reliably negative these guys probably centrally give you market exposures but they're not adding any value above and beyond what you can just give via index funds so in conclusion that's how you do a alpha analysis and how you calculate the pharma French 3 factor alpha and the standard cap in I'll post this spreadsheet on our website at turnkey analysts if you just go to the blog I'll post the video as well as the supplement Ariel and just if you have any questions just leave them in the comments so other people who are interested and figure out how to do this can also see the answer and I hope everyone has a great day and go out there and calculate some alphas and determine who can provide value and who can't

Channel: Alpha Architect

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Id: mrfWCUKX1Qw

Length: 17min 28sec (1048 seconds)

Published: Sun Oct 05 2014