[MUSIC] So in this video we're going to analyze the small-value strategy. So this is looking back historically over the last eighty years or so, what have the returns been to investing in an index fund that's comprised of small stocks that are also value in nature. And to do this analysis we're going to use data from the Kenneth R French Online Data Library which is just a tremendous resource if you want to do research in investments. And I've actually posted the spreadsheet that I use, that already has these various returns in it in case you want to kind of follow along at home or maybe even do this on your own. If you want to, great. If you don't, that's fine, I'll show you the output. The key point of this video and this exercise is just to interpret the regression output. But if you want to do the regressions yourself feel free to do so. The small value 1927-2014 spreadsheet gives you the data to do that and it's available for your use. So what are the monthly series that are in this spreadsheet that we'll be using in doing our empirical analyses in this video? So Mkt_RF is simply the return of the value-weight US stock market minus the one month US Treasury Bill rate. Mkt_RF, market return minus the risk free return. SMB, the return of small stocks minus the return of big stocks. Based on market capitalization, this is a size factor in a three factor model. HML, return of high book-to-market stocks, value stocks, minus low book-to-market stocks, growth stocks. This is the value factor in the three factor model. And then RF, we had talked about this. A risk free rate, 1-month US Treasury Bill. We're looking at kind of monthly returns and their regression. Small value is return of a portfolio of small value stocks. And then SmallValue_RF is simply the return of a portfolio small value stocks minus the 1-month US Treasury Bill rate. So the excess return of small values stocks. So if you want information on what are the classification cutoffs for size, like what's a cutoff for small, what's a cutoff for big, what's a cutoff for value, what's a cut off for growth. I refer you to this website here on the Kenneth French Data Library website. Okay, so let's fill in this table for small-value stocks. So, what's the average return? What's the average excess return? Return in access of Treasury Bills. And then let's do the CAPM model. Okay, let's do a regression for the CAPM model. What's the alpha, what's the market beta? What's the R-squared of this strategy? Okay, and remember, we're doing this from 1927 to 2014. Then let's do an analysis of the three factor model. So we're going to estimate a regression. This time we're elating the excess return of small stocks, not only to the market excess return which is a CAPM model, but we're adding the size factor and the value factor. And what's the R-squared of this regression? How much idiosyncratic risk is there? How much of the volatility of the small value stock is simply explained by these three factors here? So we know based at ahead of time that this is an index fund, a small value stocks. So once we use a 3-factor model and we're controlling for size factor and value factor, we know the R-squared is going to essentially be one because as an index fund, a small value stocks, once we control for the small and value tilled on the portfolio, we should be able to explain basically almost all the movement of this index fund. Okay, when we do the 3-factor model, what do the coefficients on the size factor? What are the coefficients on the value factor mean and this will be very useful when we interpret regression output from various studies later in the course. What's the ALPHA on the three factor model represent and why are there potentially differences from the ALPHA from the 3-factor model and that from the CAPM? All of these are question that we want to answer in this exercise. So once we estimate this three factor mode, we can fill in this table here for small value stocks. What's a three factor alpha on the 3-factor model? What are the coefficients on the various betas in the 3-Factor model. And then this R-squared, which we know should be close to one, because it's simply an index fund of small value stock. So once we're controlling for the size composition, the value composition of the fund, we should be able to explain pretty much all the movements in this index fund. What are the calculations here? And I'm just going to give you the Excel output screen shot. So if you want to do this on your own, you can see how I created these numbers. What's the average return for SmallValue stocks? What's the average excess return of SmallValue stocks? So this is just a SmallValue stock portfolio average monthly return minus the risk-free rate how does that compare to that for the market as a whole. And then what's the average kind of difference of small stocks relative to big stocks and then value stocks relative to growth stocks. So here they are all tabulated for you. It's interesting to make a comparison here. The excess return of small-value stocks is 1.2% per month. Small-Value stock portfolios is beat treasury bills by 1.2% per month. Almost double the equity market premium of the overall US stock market return in excess of treasury bills, which is about 0.65% per month. So the excess return of Small-Value stocks is almost like 15% per year, compared to the excess return of the market which annualizes about 7 or 8% per year. So we need the CAPM and 3-factor model to kind of give us some sense of what's accounting for this difference in this return. Is it due to risk? And particularly the CAPM can say hey, our small-value stocks just more sensitive to the economy, that's why they give such high return on average, or even after controlling for their beta, do they still yield great returns which means historically these stocks have maybe just been underpriced. So those who have bought them have got these great alpha returns. And then you can see over the sample period 1927 to 2014 small cap stocks on a monthly basis have beat large cap stocks by 0.2% per month or 2-3% in annul basis. Value stocks have beat growth stocks by and average of 0.45% per month or about 5% in an annual basis, okay? So there again kind of the key number to focus on and the CAPM can help tell us of this difference 1.2 versus 0.65, which is about 0.55% per month. How much of that is due to risk as measured by the beta? So let's look at the CAPM regression. Again, full information here. I just show you how do you actually estimate this regression, what are the commands in Excel to do this? Then we have the CAPM regression output here in Excel where we have the beta of 1.32 our alpha's 0.34 and our R-squared of 0.76. So zooming in on this CAPM regression I'll put you should be able to replicate this exactly if you do this on your own. Let's put this in tabulated format. So we see the average excess return of 1.2%. When we put it in a CAPM model, we see that the alpha that remains of this 1.2%, the interpretation would that 0.86% of this is reflecting the risk of the small-value stock investment portfolio. The remaining 0.34% is alpha, or the amount by which a small value portfolio has done better than expected, has beat its benchmark. So you can see small value stocks are riskier than the market as a whole given their beta of 1.33, but even after controlling for that they still have beat their benchmark by about 0.34% per month or about four percentage points in an annual basis. We also see a lot of the movement of the small-value stock portfolio is explained by movements in the market, the R-squared from CAPM regression of 0.76. We'd expect high R-squared whenever you're looking at a mutual fund, because there's a lot of stocks in it. And the small-value index fund is basically like a mutual fund of many small-value stocks, therefore it's not surprising to have this high CAPM, R-squared. Now let's do the 3-factors model regression and again, how do we do it here all laid out for you. Here's a 3-factor model regression. Few things you know there's right away, now the alpha goes to zero, the R-squared is 0.99, basically one. Big positive coefficients on the size factors as well as as the value factor here, okay? So looking at this you know three factor model regression output zoomed in here and I'd rather talk about it in the tabulated fashion here. What do we notice in differences in the 3-Factor model, relative to the CAPM model? First is, this alpha is zero, okay? So when we do the 3-Factor Model, we see that, you know, alpha now is zero. What is that telling us? In the CAPM it was positive. Well in the 3-Factor model, we're controlling for the size composition of the portfolio. The size tilt, is it more toward small? Is it more toward large? We're also controlling for the value tilt of the portfolio. Is it more toward value? Is it more toward growth? So we can think relative to the CAPM the 3-Factor model is raising the benchmark if you're tilting your portfolio toward small or value stocks and it's lowering your benchmark if you're tilting it more toward large or growth stocks. So given this is a small value index fund, we're accounting for the fact that hey, you invested in small stocks you're invested in value stocks, you should be getting higher returns. So once we account for this the alpha goes to zero. If you're a small value fund manager to earn a positive alpha, you have to be picking the best small-value stocks. If you're just investing in all the small-value stocks, your alpha will be zero in the 3-Factor model. You have to pick the best value and the best small to get an alpha in the 3-Factor Model. So we know this is a small-value portfolio. So it's not surprising there's a big positive coefficient on the size beta. This just represents when small stocks are doing well our portfolio is doing well. If this coefficient was negative it would mean we have tilt toward large stocks, because that would signify when large stocks are doing well. Our portfolio's doing well if this SMB coefficient's negative but it's positive. We know that's the case because our portfolio is small stocks. Value beta here, also positive. So that means when value stocks are doing well, on average, our portfolios doing well, but it should, right? We know it's a small value stocks. Not surprising it had this big coefficient for the three factor of value beta at 0.79. If this coefficient on the value factor is negative, it would mean that our portfolio likely has growth stocks in it, but it's positive. We know that to be the case, because it's values stocks. Then at the end the 3-Factor Model, R-squared, 0.99 virtually one. Once we count for market factors, once we control for the size and value tilt of the portfolio, we explain basically all the movement of this small, small value index fund. Whenever you have an index mutual fund you basically expect an R-squared of very close, very close to one. So I hope you found this video useful. Explaining differences between the CAPM, and 3-Factor Model. What the size and value factors represent. What the coefficient on those factors represent, and understanding why there can be significant differences in the alpha, when you go from a CAPM model to a 3-Factor Model. [SOUND]