[MUSIC] I want to give you some exercises to try and refine your understanding of how to do better with investments, given some of the concepts that we've talked through. Particularly this notion risk adjusted return. So let's start with this first investment decision. Which of these two funds would you like to invest in? Fund A has an annual return, an expected annual return of 24%. And fund B an expected return of 12%. Would you like to know something else about this investment? You ought to be asking what is the risk of both of these investments. So we've provided that to you. We say fund A has an expected return of 24%, and a volatility of 12%. Fund B has an expected return of 12%, and a volatility of 12%. The answer in this case is pretty straightforward. Fund A gives you twice as much return and a larger return at the same risk. Let's give a more difficult example. Fund A gives you an expected return of 13% and a volatility of 18%. Fund B gives you a lower return, 5% but also has a lower volatility. Fund A is twice as risky as fund B, but it makes more in return and therefore is probably the preferable investment. But what if you can't tolerate more than 9% volatility? Most efficient thing then to do would be to invest just 50% of your capital in fund A. Our portfolio basis you have a volatility of 9%. But you have an expected return of 13 divided by 2 which is 6.5%. And that's higher than that if you had invested in fund B. Here's another example. Fund A has an expected return of 5% and volatility of 6%. Fund B has an expected return of 7 and a volatility of 9%. What we are really trying to do is trying to figure out the expected return per unit of risk. So we divide the expected return by the volatility. And we typically choose the investment with the higher return to risk ratio. And normally is the better choice. But I'm now going to bring in another complication which is important, the risk free asset. So the usual question here is, which we just went through, fund A and fund B, fund A with an expected return of 8% and volatility of 3%. Fund B with an expected return of 13% and volatility of 10%. And the usual answer would be to take the expected return and put it into risk and by that measure fund A is preferred to fund B because it's expected return for united risk is higher than that of fund B. But now let's complicate the matter a little bit by putting a risk free asset in the next. And so we have a choice r a government bond instrument yielding 6% with no volatility. What we need to do is transform these returns into excess returns, because after all you can always get a risk free investment. In this case we are assuming we get 6%. No through any of the G7 Countries of this point in time but maybe through in certain margin markets. We need to transform these returns into excess returns. An excess fill space what you have is fund A, it gives you a 2% excess return. Fund B gives you a 7% excess return. And the volatility remains the same. And now, if you look at the expected excess return per unit of risk, fund B actually has a slightly higher number than fund A. Best risky investment is therefore B. It used to be A, but that was only when you ignored the risk free rates. Once you put in the risk free rate, that choice changes. The risk free rate matters. And the question you must always ask, what is the excess compensation for taking risk? And [INAUDIBLE] [MUSIC]