In the last video, we adopted an optimal portfolio allocation to integrate your financial constraints. In this video, we continue to add step by step layers of complexity, to improve on our basic allocation and make it more realistic. Remember that all portfolio management techniques follow the same template. They maximise a preference metric, subject to financial constraints, and the model of how financial asset returns are generated. In this video, we focus on the third aspect: how can we use a model for how financial asset returns are generated to improve our portfolio allocations. Optimal portfolio allocations, as discussed in the first video of this lesson, more often than not underperform in real life. One major problem is the difficulty in precisely estimating the required inputs that is expected returns, volatilities and correlations. We saw in the last video that integrating financial constraints has the benefit of controlling for errors made when estimating the expected returns, volatilities and correlations. But despite this improvement, portfolio allocations are still extremely sensitive to the expected returns we use. We need some help from the field of asset pricing, which is the area of economics concerned with understanding how investors' preferences and the structure of financial markets determine financial asset prices. Understanding these components is crucial to portfolio management. They explain how prices are formed in financial markets, and what will be the determinants of each asset's expected return. Researchers in the field of asset pricing ask what happens in equilibrium if all investors choose their portfolio, using techniques such as the one seen at the start of this lesson. Equilibrium here is defined as a situation where prices are set in the market, so that there are no unsold assets. The outcome is an asset pricing model that expresses the determinants of expected returns as a linear function, or close to a linear function. In this equation, the expected excess return has several components. The first is a set of risk factors F, that capture common or systematic sources of risk in the economy, for which investors receive compensation. The first of these factors Fm, is the market portfolio that contains all assets. Then the betas govern how one asset is exposed to these factors. A higher beta for the market factor, for example, indicates that a security moves more in tandem with the market than a different security with a lower market factor beta. For example, Walmart, a safe stock, has a market beta of about 0.5, while Amazon, a riskier stock, has a market beta of about 1.5 The third component, alpha, is what we call a mispricing: the portion of expected returns that cannot be explained by exposures to risk factors. The alpha is a constant, for example 2% per year. A positive alpha implies a higher return every period, regardless of other factors. For example, a hedge fund manager outperforming the market, because his expertise allows him to better identify mispriced securities. It is called a mispricing because it is literally a free lunch. The fierce competition among all investment professionals makes it very hard to identify a security with a positive mispricing. How useful is an asset pricing model? By using such a model, we integrate some economic foundation in our portfolio management approach, instead of simply estimating the expected returns as free parameters. We can estimate the average return of known factors and the betas of an asset to these factors, in order to obtain the asset expected return. In the most basic setup, called the capital asset pricing model or CAPM, the market portfolio Fm, in which all assets are weighted by their market capitalisation, arises naturally as the only source of positive average returns. There are no mispricings nor other risk factors. According to this model, the market portfolio is the only factor, and only the differences in exposure to the market factor explain the differences in expected returns across portfolios or securities, such as Amazon having a higher expected return than Walmart. This is an important theoretical finding with long-lasting impact. We have become accustomed to think in terms of this market portfolio. For example, when we ask "Did a fund manager beat the market?", we implicitly compare his performance to what the CAPM tells us. However, more than three decades worth of academic research has shown that we live in a multi-factor world. Assets' expected returns are related to more than only the market factor. In the stock market we have decades of evidence showing how value stocks, stocks that have a low price compared to their accounting value tend to outperform on average growth stocks, which are stocks that have a high price compared to their accounting value. In the currency market, we have what we call the carry factor. Forward contracts of currencies in countries with high interest rates tend to have higher returns than currencies with lower national interest rates. Some factors are even important in multiple markets. Like momentum, the tendency of assets that have been trending up recently to have higher returns than those that have been going down recently. This factor appears to generate excess returns in all asset classes. For example, equities, commodities or currencies, and even across all geographic regions. An asset pricing model, which is a good representation of reality, is invaluable. First, it tells us what our optimal allocation should look like. Indeed, if only risk factors are compensated with positive expected excess returns, then we know our optimal portfolio should be a mix of these factors. We will come back to this aspect when we discuss quantitative active management strategies in module 3. Second, a good model allows to evaluate the performance of an investment product or a fund manager. Indeed, the fund should create a positive alpha or offer us a set of risk factors to which we do not have access, in order to justify the management fees that we pay. This point will be important when we discuss active management methods in module 3, and when we do performance evaluation in the first lesson of module 4. So let's wrap up with one question: decades of research in finance have shown that: a) the only risk factor is the market portfolio b) there are multiple risk factors in markets and they represent risk-free sources of returns called mispricings, or c) there are multiple risk factors and they represent different sources of systematic risk. The answer is c. There are more than one risk factor in financial markets and each factor is the reward for bearing one kind of common risk. Thus, portfolio allocations are sensitive to assumptions on expected returns using an economic model for asset prices, bring some economic content and leads the better performing portfolios. We now move to the second lesson of this module, one that will look at more specialised portfolio management techniques.