He who knows not and know knows not that he knows not is a fool, avoid him. He who knows not and knows that he knows not is a student, teach him. He who knows and knows not that he knows, is asleep, awake him. He who knows and knows that he knows is a wise man, follow him. Through all five weeks we were talking about, first of all, how to distinguish between those who knows and those who knows not. The second, what to do if you believe that you know something on the week three and week number four. Now let's talk what to do with all that things and we'll start with full indexation or actually, with indexation as an approach. When we are using indexation, when we believe that market is efficient or we believe that exploiting inefficiencies would be too costly. For example, I'm a Portfolio Manager in Russia and my portfolio is bench-marking to my 650. I'm not paid for exactly making return bigger than return on my 650. I'm paid for just matching my 650. That's why my job is to just replicate that portfolio. The structure of my 650 is open. It is easily feasible in case if I have enough funds at my disposal. In some cases, the minimal unit for replication of index is too big. For example, let's look at S&P 500. The minimal unit is unfeasible for most of private investors. It is unfeasible even for some institutional investors. Then we have the situation of, for example, we'll share 6,000 stocks. The minimal unit is high, but more to it, most of these stocks are illiquid. That's why even if I have enough funds at my disposal, the very process of replication is impossible. What can I do in that case? Well, two approaches. One is called stratified sampling, so I am dividing my universe by some number of factors? For example, for me, it is important to distinguish between two factors basically, the factor of size and the factor of style. Here we have famous Morningstar style box. In my universe, all stocks could be divided into nine kinds. Large value, large blend or large core, large growth, medium value, blend, and growth, and small value, blend, and growth. Now, I am dissecting my universe and I am learning what is the structure of my universe or my index in terms of these two dimensions, large, medium, and small, value, blend, and growth. Then I'm taking in each dimension two most liquid or most cheap stocks. Instead of 6,000, I have only 18 stocks and that makes my index more replicatable. Let's call it so. This is the essence of stratified sampling. I am just first of all, building the structure of my index or learning the structure of my index in terms of several dimensions which are important for me. Then I am recreating that index using lower number of instruments with desirable characteristics. For example, it would be instruments of higher liquidity, instruments which are cheaper and easier to implement. But, my portfolio would maintain the same structure in terms of these dimensions which I have learned previously. This is stratified sampling approach. Now the second approach is optimization. In case of optimization, actually doing the same. I have factor model and I am looking at exposures of my benchmark to different factors and actually my goal is just to replicate exposures in my portfolio. I am building portfolio with constraints on number of positions, for example, but I am targeting a certain exposures, the same as exposures of my target benchmark. This is the essence of optimization. What drawbacks do we have here? Of course, full indexation is the optimal way of indexation. In some cases, it is unfeasible due to liquidity and the size of minimal unit. As a drawback of optimization and stratified sampling, we have such thing as tracking error. Basically I have as a passive manager, as a manager which believes that there is no reason to significantly deviate from the index from my benchmark. I have to keep my tracking error as low as possible. If I would build some optimizational portfolio or I would do portfolio using stratified sampling routine, probably my tracking error would be quite high. My goal would be to minimize the tracking error. But there are no such things as a free lunch. For the possibility of replication, you have to pay by tracking error.
