Fama French 3 Factor Model

hi today I'm going to go over a brief in overview of the fama French three factor model you may be familiar with the capital asset pricing model and it's use of one factor the market premium or the market risk factor what the plumb a French three factor model does is it includes an additional two other factors to calculate the required return on equity the factors for the former French three factor model include the market risk premium which is the premium that's included in the capital asset pricing model but it also includes a size premium because in their research they found that small firms tend to have higher returns or require higher returns than large firms because they're riskier and then the value premium which shows that that firms that are have high book to market values or low market the book values those might be undervalued in the market tend to earn higher returns to that just like in the capital asset pricing model we add a risk-free return to calculate the required rate of return on equity using this model the way that it works is it looks something like this where we the return for the individual firm is equal to the risk-free rate plus a beta or a correlation coefficient for the market which is the this is the market risk premium that you you might be familiar with the notation here stands for the return for the market less the return on the risk-free asset plus a correlation coefficient of beta for the size of the firm and and this second item is a SCI's premium it stands for a small - big so small the return on a portfolio is small firms - the return for a portfolio on big firms and then finally the last one is the value premium the the beta is the correlation coefficient for the value risk premium and the value risk premium is calculated as the return for portfolio of high book to market value stocks - the return on a portfolio for low book to market value stocks the betas are calculated for each firm using multivariate regression and I'm going to give you an example of that in a minute and then so we calculate the betas and we multiply them by these risk factors which which will be provided for you in this tutorial so for an example after we calculate the correlation coefficients for each of these risk premiums we can then calculate the required rate of return for the stock in this case we have a risk-free rate of 3% an equity risk premium of 5% so in terms of the capital asset pricing model this would be your beta or excuse me this would be the premium on the market the beta in this case would be the beta from the capital asset pricing model however we're not going to calculate it the same way again we're using multivariate regression to include the effects of including the size premium and them and the value premium in the regression so the size premium would be 2.2 percent in the size beta the sensitivity of this individual stock to the size premium or the size risk 0.12 a value premium of 3.8 and again think of that as that risk premium that we we often use for the capital asset pricing model and then a value beta again this is the sensitivity of the firm to that value premium in that value risk so our calculation is pretty straightforward after we calculate the correlation coefficients we can then multiply them by the risk premiums 5% two point two percent three point eight percent to get the required rate of return for the firm using the fama French three factor model the benefit of the vomer French through factor model over the capital asset pricing model is that it includes these size and and value premiums that aren't captured in the the capital asset pricing model research has found that this tends to be a little better estimate for for the cost of equity for firm and so now what we're going to do is now what I'm going to do is give you an example of calculating the fama for industry factor model so I put together a spreadsheet this spreadsheet is from Kenneth French's website Kenneth French is half of the partnership of fama in French and he updates these risk premiums and these four for the three-factor model on a monthly basis what we have here are the monthly premiums through the beginning of October 2012 so you can think of this data as October 1st 2012 and so the negative one point four four percent is the market return minus the risk-free rate between September 1st 2012 and October 1st 2012 Kenneth French and Eugene fama calculate these every month based on again in the first case this is the size Premium small - big and they take a portfolio of small firms and subtract the return from a portfolio of big firms from that to get the size premium and this is the high minus low or the value premium and in what they do is take a portfolio of high book to market value firms and subtract the return from that port subtract to return from low book to market value firms from the returns from the high market book to market value firms to get the risk premium finally we have a risk-free rate this is the monthly t-bill rate for that for that month and what we're going to do is kind the returns for a specific stocke calculate the excess return and so this is a little bit different than how we calculate the capital asset pricing model but we're going to calculate the excess return for the stock over the risk-free rate and then regress that on these three variables so the company I'm going to use is forward so what I'm going to do is go out and get the returns for Ford stock and as I mentioned before the returns from the fama French model that that are provided by Kenneth French the the dates are for the kind of the return for the preceding month so the the return for October 2012 is the return from September 1st to through October 1st so I want to match my dates up with that and I'm going to use five years of monthly returns so my start date is going to be September 1st 2007 and my end date is going to be October 1st 2012 so once you do download those you'll you'll get something like this I'm going to download this to a spreadsheet and so this is what it gives me this is the spreadsheet for Ford returns again they end October 1st 2012 the open on October 1st 2012 was nine dollars and 89 cents the low the high was 10 8.08 the low was nine point eight eight the close was nine point nine three this is the volume of shares traded that day and what I want to use is actually the adjusted closed what the adjusted closed does is it includes the effect of dividend payments so it includes what we refer to as the total return the return from both the increase or decrease in the stock price plus the effect of paying the dividends so it's going to include that dividend yield in the in the end prices or the in returns that we calculate so I'm going to go ahead and calculate the returns for this period the way I do this is I put in the Excel function Ln for natural log so I'm going to take the natural log of the most recent price divided by the price in the prior period and that gives me a compounded return it's very similar to the holding period return that you might be familiar with which is the adjust - close - the previous suggestive close / the previous suggestive close the difference between the two is that this the natural log assumes constant compounding of the returns and tends to be a little bit more accurate so I'm going to go ahead and pull that down all the way the last one there's give you an errors we'll take that out and then we're going to copy and paste that oops want that let me try that again they're copied and pasted the values this is for Ford I make it look nice now I'm going to calculate the excess return note because what we're going to do is regress the excess return on our three variables so the excess return is equal to the return for Ford - the risk-free rate for the period so now what I'm going to do is complete my multivariate regression to do that you may need to go out online or excuse me not online you may need to go out and actually add the tool pack for the data analysis toolpak if you've already got it in there you can select data and go to data analysis what I'm going to do is go out here just to show you how to access it you'd want to go out to options so I press it on file and then options and then go to add-ins go down here to a manage Excel add-ins and if it's not already checked you'll want to check analysis toolpak that will give you access to data and data analysis so in data analysis I want to go to regression so I'm going to scroll down to regression and press ok my Y input range will be in my case G 1 and then notice that I'm highlighting the label and I'll show you why when we actually calculate the regression now pull that down all the way and then for the X input range I'm going to select B 1 which is the market risk premium through D 1 which is the value risk premium and pull that all the way down to the end of my time period and then you want to select labels that's why we highlighted the labels of the top so that our results are labeled once you have that your screen regression screen should look like this and this gives us a result our results on a new page so those coefficients that I mentioned before are these values here the R square is provides a statistic on how well the model actually fits the returns that we see the actual returns we for Ford it's not great this model model predicts about 41 percent of the variation in Ford's return so it's not it's not great it tends to perform a little bit better than the capital asset pricing model though alright so the last step is to actually calculate the required rate of return for Ford stock so the first thing we want to piece of information we want to include is the risk-free rate and I use the yield on the 10-year US Treasury I use the yield on the 10-year US Treasury because I see its stock as a long-term investment and I want to match my risk-free rate to my expected investment horizon so I'll go out to Bloomberg comm to get this piece of information I go to market data and US Treasuries and the yield on the US Treasury is currently one point five seven percent so we'll include that here and then the first item is the market risk premium so I'll start off by including the market risk coefficient that we calculated and that would also you could also call that the beta and that's equal to the coefficient for the market risk excuse me the market return minus the risk-free rate or the market risk premium for Ford this is high and it's high because they are sensitive to interest rate risk because they have a lot of debt and it's high because they're also sensitive to fluctuations in fuel prices and unemployment the market risk premium that I'll be using is five and a half percent and this is based on the market risk premium for the time period 1980 through 2006 I like that cutoff date because it precedes the housing market bubble bust and the resulting recession so it represents a more normal time in the marketplace just formatting that a little better the second premium we're going to use is the size premium so I'm going to clear the size risk coefficient that's going to be equal to 0.03 6 937 the size risk premium that I'm going to be using as point O 2 again it's it was calculated between 1980 and 2006 all right so we have the risk-free rate the market risk premium and the size risk premium included the last item is then the value risk premium we'll add in our value risk coefficient and that's going to be equal to 0.5 3 8 and then our value risk premium which is equal to 0.04 3 where I got the this information for the market risk premium the size risk premium and the value risk premium is a textbook called equity asset valuation the authors are Gerald Pinto Elaine Henry Thomas Robinson and John Stowe it's the second edition of the book and it's publication date is 2010 in case you need to cite that anywhere in your report so using all this information we can calculate the required rate of return for Ford and that's going to be equal to the risk-free rate plus the market risk coefficient multiplied by the market risk premium plus the size risk coefficient multiplied by the size risk premium plus the value risk coefficient marked x the value risk premium which gives us an answer of fifteen point four eight two percent and that's it that's how you would calculate the required rate of return using the farm of French three factor model a couple of other things to point out is the information here on the P values for Ford we see that the market risk premium is statistically significant it's very small however for the size and the value the the P values are quite large and art would not be considered to be statistically significant please let me know if you have any questions I will send you a link to this data for them the market risk premium the scisors premium the value and the risk-free rate along with this video Thanks

Channel: Shane Van Dalsem

Views: 106,913

Rating: 4.8796992 out of 5

Keywords: Equity Valuation, Fama French

Id: HFTOX6a4FAQ

Length: 20min 16sec (1216 seconds)

Published: Thu Dec 06 2012