In our last session together we examined some of the key evidence concerning the link between risk, as it's captured by the Capital Asset Pricing Model, and the actual realized returns observed for risky assets over an extended period. In this session we're going to consider some suggested extensions to the CAPM that have arisen from that early empirical work. And then we'll go onto examine some survey results that provide details about the discount rates chief financial officers actually use in practice. First though, a quick recap of the evidence so far. While the CAPM is an intuitively appealing model, which suggests that there is a single source of systematic risk for all risky assets, and that that risk is captured by the asset's beta, the problem is that the evidence concerning the link between beta and returns is, well, to say the least, quite weak. Specifically you will recall that Eugene Fama and Kenneth French demonstrated that when they placed U.S. listed companies into portfolios according to their beta, and then tracked subsequent performance, they found no evidence that high beta stocks outperformed low beta stocks. On the other hand, when they formed their portfolios in either size, as measured by market capitalization, or on the basis of the ratio of book to market value of equity, the results are very strong. Specifically, they found that smaller firms earned higher returns than larger firms and value firms, that is firms with high book-to-market values, earned higher returns than growth firms, those firms with low book-to-market values. As previewed in our last session together, this has led to the development of multi-factor models. Multi-factor models that include pricing factors relating to both size and book-to-market values. So here is the Fama-French 3-factor model. It is essentially a modified CAPM that includes two additional factors and two additional risk measures. Working from the left hand side of the equation, the first thing we notice is that we've brought the risk free rate of return over to that left hand side of the equation. Now this simply implies that the three factors on the right hand side explain the additional compensation that investors can expect over and above the risk free rate of return. The first factor on the right hand side of the equation is simply our standard market risk factor with our standard plain vanilla beta included. The second factor is a size factor, where beta SMB is measuring the sensitivity of asset iâs returns, to a portfolio that mimics, that is, follows a bought position in small stocks and a sold position in large stocks. Now, intuitively, you can think of this as the extra return that you can expect from a portfolio of small stocks, over and above a portfolio of stocks in large companies. The final factor is the book to market factor where beta HML measure the sensitivity of asset i returns to the returns of the portfolio that mimics a long position, a bought position, in a portfolio of stocks with high book-to-market ratios, and a short, or sold, position in a portfolio of stocks with low book-to-market ratios. So, you can see this three-factor model is designed to address the apparent anomaly discovered when it was found that the standard CAPM on its own was unable to explain much about the cross section of stock returns. So is that where it all stopped? The answer is no. As you might expect, following the work of Fama and French, the hunt was now on for additional pricing factors that might help to explain the cross section of stock returns. A couple that have gained traction over the years include a momentum factor that accounted for the observation that recent stock price performance was often a good indicator of future stock price performance in the short to medium term. Another factor that gained prominence was the liquidity factor that was linked to the finding that companies that experienced higher variability in trading volumes had higher expected returns. Now this result was consistent with liquidity risk being priced into the market. Then more recently in the last couple of years, we've seen other factors suggested, including investment and profitability factors. So this is a literature that we can safely say will continue to evolve along with our understanding of what it is that drives prices in markets. But, let's take a step back for a moment. Recall that what we are trying to do here is come up with a model that explains what returns investors expect from assets, given their risk profile. Well, why don't we ask a subset of very important market participants, that is chief financial officers, what it is they use to estimate discount rates in their day to day operations. So John Graham and Campbell Harvey did exactly that when they surveyed 392 CFOs from Fortune 500 companies in the U.S. asking them, how do you determine your firm's cost of equity capital? The number one answer was the CAPM approach. With more than twice of many managers using the CAPM than used a multi-factor model even though as we saw, multi-factor models might be better able to describe patterns in realized returns. But when you think about it, perhaps that's not really the question we want to ask. You see, Graham and Harvey were asking about the estimation of the cost of equity capital. Now, that's a useful measure if you're going to do things like value the company shares. Because the CAPM will give you the discount rate that you can use to discount, for instance, the expected dividend stream from the shares to arrive at a valuation for the share. However from the firm's point of view, the question we'd really like to ask is how do they arrive at the discount rate that is necessary to discount the expected cash flows of new projects that they're attempting to assess. Now Les Coleman, Chris Maheswaran and myself, we did exactly that when we surveyed senior financial managers of Australia firms and asked them how frequently they would use different discount rates when assessing new projects. Now let's pause for a second. Everything we've done up to this stage, in this course, would lead us to expect that managers would nominate the risk matched discount rate for this particular project choice because this is exactly what our elegant theories and beautifully presented textbooks have been telling managers for years. That is use a discount rate that reflects the risk of the project. But no, the most popular response received was the discount rate for our entire company. Oh dear. Now, this is the sort of result that potentially has an academic reconsidering their life choices. I mean, seriously, what good is it playing the role of sage on a stage if no one is listening? Then I remembered the concept of weighted average cost of capital and I started to feel a little better. You will see why in our next module together. So, there we have it, in this session we described one of the first, and definitely one of the most widely known and used multi-factor asset pricing models, the Fama-French three factor model. We also discussed how it had been further augmented to account for other return patterns observed in markets. We then detailed key empirical evidence that gave us an insight into what financial managers actually use when estimating their own cost of equity, as well as project-specific costs of capital. More generally in this module we have differentiated between unsystematic and systematic risk, highlighting how an appropriate measure of systematic risk is captured by beta. This led to a discussion of the capital asset pricing model, where we also discussed the appropriate way of dealing with systematic risk in a portfolio setting. Our next set of sessions dealt with the empirical evidence on the performance of the CAPM, highlighting its lack of explanatory power of realized returns when benchmarked against size and book-to-market factors. We've now concluded with the discussion of multi-factor models, and what amounts to a blatant teaser of the next module in the course, where we will think about how firms use financial information obtained internally within the firm, to estimate a firm-wide cost of capital. What we call a weighted average cost of capital. Cheers.