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Â And the way we're going to start this session is by looking at three

Â hypothetical assets and the reason why they're hypothetical you're going to

Â understand a few minutes from now, I need it to behave in a certain way.

Â and, and that is what were going to see in just a minute.

Â So there you have ten years, three assets and lets think of those as annual returns.

Â It doesn't matter whether these are Dollar returns or

Â Euro returns, whether this is our total returns or,.

Â Just the capital gains.

Â Just think of these are the annual returns of the assets.

Â And if you want to draw a parallel,

Â to the data that we've seen in the previous session.

Â You can think of those as being total returns and

Â all of them measured in In terms of Dollars okay?

Â And as we've done before.

Â We can calculate the arithmetic mean return.

Â Simply by adding up all those observations and divide it by ten.

Â And we can calculate the volatility of those assets in a,

Â in a little more convoluted way but you're going to find again the expression for

Â that in one of the two technical notes that goes with the first session.

Â By the way, that brings it to a point that this session is also going to

Â be complemented by a technical note, and that technical note will help you in

Â the calculation in the implementation of the measures that we're going to discuss.

Â Here, as we did in session one, we're going to try to magnify the intuition.

Â We're going to focus on understanding the concepts.

Â And then the actual application of the concepts, then you're going to

Â go into the technical notes, look at the formal expression, and then you're

Â going to try to work out a problem set that will evaluate whether you understood

Â the concepts that we discussed in both session one and session two together.

Â Because again, these are sort of two sessions running into each other.

Â So back of the, back to the data that you have.

Â In front of you, we have three assets over ten years.

Â And as you see, you know, those assets, as any others, fluctuate over time.

Â They give different, mean returns.

Â In other words the average return over those last ten years has been different.

Â Has been quite a bit higher for asset three than for asset two.

Â And quite a bit higher for asset two.

Â Than for asset one.

Â But they also have very different volatility.

Â So acid one fluctuated quite a bit.

Â There are no negative returns there in any of the three assets.

Â It doesn't really matter.

Â But there are no negative returns in any of the three assets.

Â But acid one, as measured by the standard deviation of

Â 10% fluctuated a lot more than asset three.

Â And asset three as measured by the standard deviation of 5%, measure

Â fluctuated quite a bit more than asset two, which has a volatility of 1.5%.

Â And remember that's the way.

Â That we use this measure of volatility to evaluate uncertainty and

Â variability in relative terms so we can say that asset one fluctuated a lot

Â more than asset three which fluctuated a lot more than asset two, and

Â therefore when I look ahead I have much more uncertainty.

Â About what returns I can get in the future when I invest in asset one than when I

Â invest in asset three, and then when I invest in asset three compared to when I

Â invest in asset two so we're not going to go back to the interpretation of those,

Â mean returns and volatilities, but we can calculate those mean returns and

Â volatilities and what that actually shows you is that the most volatile asset of

Â the three was asset one and the least volatile of the assets.

Â Was asset two.

Â Now, remember that what we want to do with this is to combine them in a portfolio.

Â And we're going to focus on two portfolios that combine these assets.

Â And the first portfolio in which we're going to focus.

Â Is a very specific combination of asset one and asset two.

Â And I say a very specific combination because the propotions of our

Â money invested in asset one and asset two have been very carefully calculated, and

Â you'll see in a minute why.

Â They have been very carefully calculated.

Â But we're going to consider that whatever capital that we have, and

Â it's important that it doesn't matter whether you have $100 or

Â you have $100 million, we're going to be thinking in terms of proportions.

Â In finance, and particularly in portfolio management,

Â we always think in terms of the proportion of your capital.

Â So it's not about how much money you have, but

Â it's actually how you split whatever amount of money.

Â You may have.

Â And so in this particular case,

Â we're going to think about building a portfolio with asset one and

Â asset two in very specific proportions, which are putting 13% of our money

Â in asset one and 87% of our money in asset two.

Â Now how would we calculate the return of our 13% in asset one,

Â 87% in asset two portfolio on an annual basis?

Â Well, that is very simple, and the reason it is very simple is because the return of

Â a portfolio in any given period is equal to the weighted average return.

Â Now we weighed average return by definition means the returns of each

Â asset in the portfolio multiplied by the proportion of each asset in the portfolio.

Â So if I multiply asset one had a return of 25%, and

Â I'm putting 13% of my money in asset one so 25% multiplied by 13%.

Â And asset two delivered a return of 21.3%,

Â and I'm putting 87% of my money in that asset.

Â So now, 25%, returning asset one, multiplied by 13%, proportion

Â of my money invested in asset one, plus the same for asset two, that is 21.3%.

Â Return of asset one multiplied by 87%.

Â my, the proportion of my capital in asset two,

Â that gives me the return of the portfolio in year one.

Â If I do that, over, and over, and over again.

Â For the ten years for which we have information,

Â then we're going to end up with ten annual returns for

Â a combined portfolio that is invested 13% in asset one.

Â And 87% in asset two.

Â And here comes the really interesting thing.

Â If you actually do those calculations year after year after year, magic.

Â You're going to get a portfolio that gives you exactly the same return give or

Â take a decimal by exactly the same return of 21.7%.

Â Now let me first show you a picture.

Â That picture the blue line is actually the return of asset one.

Â In the ten years that we have information.

Â The green line is the return of asset two in the ten years for

Â which we have information.

Â And you can guess what the black dashed line is.

Â Is basically the return of the portfolio fixed at 21.7%.

Â Now it sounds pretty interesting.

Â Doesn't it? That you actually put together two things

Â that are volatile.

Â Two things that fluctuate over time and

Â you end up with something that is not volatile.

Â That has no viability over time.

Â Well, this is the magic of diversification.

Â Before we get there we have one more thing to explore.

Â But one thing that you should keep in mind for

Â now is the fact that you are putting together.

Â Two assets that have fluctuated over time.

Â And we end up with a portfolio that has not fluctuated over time.

Â Now we're going to do another combination.

Â We're going to go back to assets one, two, and three that we saw at the beginning.

Â But now we're going to combine assets one and three.

Â Alright? And were going to do it in this case,

Â it doesn't really matter the proportions.

Â And because it doesn't really matter, which is going away to pic 50-50 so

Â were going to put 50% of our money in asset one, and

Â 50% of our money in this case, in asset three.

Â All right? So you see the returns of asset one.

Â You see the returns of asset three, and now you know how you calculate

Â the portfolio in each of the return of the portfolio, in each of those years is

Â 50% times a return of asset one, plus 50% times a return of asset two.

Â So for period one.

Â That would be 25% multiplied by 50% plus 32.5% multiply by 50%.

Â That's going to give you the return of the portfolio in year one.

Â And if you keep doing that over and over again.

Â Over the ten years for which we have information.

Â Then we're going to end up with the return of a 50/50 portfolio in asset one and

Â asset three.

Â And when you look at those returns.

Â