0:47

Revisit our two asset choices and the move onto three.

Â And more.

Â Was combining Google and Yahoo a good choice?

Â And I don't want you to do numbers, if you have the numbers great, great.

Â If you can figure out the standard deviation of

Â Google and Yahoo and the relationship between the two,

Â just substitute them in that formula, take that opportunity.

Â To try to see what's going on. So, I'm asking you intuitively, though.

Â Do you think, "Was combining Google and Yahoo a good choice"?

Â Of course, your answer should, first question should be, "Hey Bozo.

Â What do you mean? Relative to what?

Â Well, Mr.

Â Bozo says the following. Just use your

Â head Bozo and try to think about it.

Â So, the thing I'm asking is quite straightforward obviously.

Â And, but, but kind of hidden is, could you

Â have made a better choice, given that you invested /g.

Â And I think probably yes, and the reason is,

Â Google and Yahoo are roughly in the same space.

Â Yahoo is much smaller, but let me say that Yahoo is probably

Â 2:13

Would Google and Boeing be a better choice?

Â Again, do the analysis.

Â This is your week of running with all the examples you can.

Â It's my week of showing you the beauty of what's going on.

Â I'm not going to use too many examples.

Â I'm going to use real data in the real context.

Â But for now, and I've already assign with real data,

Â try to do this. But intuitively, what do you think?

Â It's a better choice? Chances are, yes.

Â They are very different industries, they're doing

Â very different things, and therefore chances are, they'll

Â have a lot of things specific to each

Â other, which is the first sign of diversification.

Â Common things?

Â No. Specific, yes.

Â 3:12

Is it a good choice? Mm, I don't know.

Â Certainly better.

Â Intuitively.

Â Do the numbers if you The risk of the portfolio is affected by how many factors?

Â Portfolio. It's gone from one to two assets.

Â Factors have gone to four, why?

Â Let's just wrap up. The four factors are

Â sigma, a,

Â b, 2 a b. So there are four factors.

Â One standard deviation of a times division of b.

Â Two standard deviations or two variances but two relationships.

Â 3:58

Why are these different than the average risk of the two assets held in isolation?

Â So, if I held only one, it would be this risk.

Â The second this risk.

Â And what's the average of the 2? Weights average, very simple.

Â Why is the average risk of the 2 held in isolation different?

Â Because of this.

Â Or, if you like to think about it differently because of sigma ab.

Â Many people prefer

Â to think about correlations rather than covariances.

Â And I think you know the relationship between the two.

Â One is standardized and easy, intuitive.

Â No there's not.

Â I love covariances as much as I love correlation because, which comes first?

Â Correlation doesn't have a hope because

Â covariance comes first, tells you the sine.

Â It suffers from units and magnitude problems, so you scale it.

Â By what? How do you go from here to here.

Â One more time. You just scale this by sigma a, sigma b.

Â 5:10

Suppose you have three securities in your portfolio.

Â Google, and you dropped Yahoo.

Â No, nothing against Yahoo, just from

Â a diversification st, st, st, eh, perspective.

Â So Google is the internet domain.

Â And to be honest with you, I sometimes wonder what it does, because

Â [LAUGH]

Â it's a river, but obviously it's not the way it used to think in the past.

Â It's not a physical commodity like Boeing.

Â What does Boeing do?

Â Man/g, huge physical things, planes. Google?

Â Huge!

Â But I don't know what.

Â That's what's fascinating and troublesome at the same time.

Â And Merck, well, it's a very different animal.

Â What does Merck do? Merck produces

Â medicines for people.

Â Is it the same business as flying or being all over the Internet?

Â No.

Â So I'm picking three very different securities.

Â 6:23

Again, something for you to do, and put in the table where they were not.

Â Remember the table we started off this

Â morning and left off last, week, that table.

Â Try to substitute stuff as you calculate it, okay.

Â Go, you may find it on the web.

Â 6:43

[LAUGH]

Â The standard deviation still, let me assure you can, if you look hard enough.

Â But try to calculate too.

Â It turns out, we'll see, that Yahoo Finance gives

Â you historical data, in order to be measured as

Â well as say, for example, Morning Star, but it's

Â free and you can do calculations and you can do

Â [INAUDIBLE]

Â ,

Â [UNKNOWN]

Â and so on. So how do you measure the risk of each?

Â Sigma g.

Â 7:33

How many securities do I have now?

Â Three?

Â And still I'm not, sorry, I jumped ahead, I don't want to show

Â you the answer, I want to talk about it before we go there.

Â It's going to look nasty, and nastier than what the two-one was.

Â Not as simple, clearly much more nasty than one asset, right?

Â One asset is very simple. Standard deviation

Â of Google, or Boeing, or Merck. Now we're combining the three.

Â So, what are the first thing you have to think about when you have not only

Â that I've chosen Google, Boeing, and Merck, but

Â what do I have to think about right away?

Â 8:07

I have to think about Xa, Xb, Xc. What are these?

Â These are the proportion of my investment going into the three.

Â So, suppose you look at the importance of this.

Â Suppose I am diversifying slowly, right?

Â But, this is 0 and this is close to 0. Have I diversified?

Â I haven't.

Â So, the rates are very important, having three securities

Â superficially, in your portfolio, this is close to zero.

Â And suppose this is 90% of your rate.

Â 8:41

You haven't really diversified, so the proportion of relative putting in

Â each is very important and it's not the case that you put equal every time.

Â I'm just giving you a sense of what's going on.

Â How would you measure the risk of your portfolio?

Â Think intuitively.

Â How many, and we'll revisit this issue over and over, what will matter?

Â These three clearly will matter, but what will matter to?

Â 9:12

Relationship between a and b in terms off in the data.

Â It's also the relationship between b and a.

Â So the measurement of the two are likely the same thing, within a

Â certain set of assumptions we have made. What

Â else? Sigma ac and sigma ca.

Â Finally, what/g? Sigma b c,

Â sigma c b. So,

Â we have, I've shown you all the elements. The rates are extremely important.

Â The personality is called standard deviation's are very important.

Â But, what is more, what is also important is relationships.

Â Okay, so see,

Â you'll see a pattern in a second.

Â So I'm going put up this genetic equations, every

Â time I do equation, there will be a list of

Â equations for risk and return like I did for

Â time value of money, will be on the web site.

Â But, just stare at this, I know it's a

Â little bit intense, there're a lot of terms going on.

Â Let's start off and let's just walk through this a little

Â bit slowly.

Â Is this any surprise, remember the squares are simply because variances are squared.

Â No, when would I have only this as my risk when x is 1, all my relevant 1.

Â This is the second personality, second variance.

Â Third variance. I told you these will appear.

Â But now, how many relationships are there? Two between a and and

Â b, they are the same because sigma a, a b is

Â equal to sigma b a. Two between a and c and two between.

Â B and c. Whatever I've done going from

Â [UNKNOWN]

Â one to the next.

Â The first term is the same, the second term

Â is the same, the third term is the same.

Â The, actually turns out all terms are

Â the same except starting with covariances and replacing.

Â Covariance by

Â correlation. And remember again, what is Rho ab?

Â Correlation is equal to sigma ab over sigma a times sigma b.

Â And I'm using this to substitute. And that's simply because

Â [CROSSTALK]

Â 12:26

We'll take a break again after this because we're going

Â to jump to, after this specific, we'll jump to a

Â lot of assets and then take a break because that's

Â a good time to get a sense of what's been happening.

Â How many unique variances?

Â Since we have done this, I'm going to go a little bit faster.

Â But I'll do a video. And this is a good thing to guess.

Â Three, don't forget weights.

Â Because if one of the weights is close to 0, it's two so it matters that you

Â [INAUDIBLE]

Â . How many relationships?

Â 13:23

But that I mean

Â how many

Â terms

Â going

Â on? How many relationships, what did I say, 6.

Â Think about this, AB BA, 2, AC CA, 4, BC

Â CB, 6. In a room with 3

Â people, how many relationships.

Â 14:03

Just do this. A, b, column abc.

Â You'll have six relationships.

Â And turns out, in the data in between under

Â our assumptions, what happens is there are three unique.

Â Why?

Â Because ab, sigma ab is equal to sigma ba. These are the first two.

Â Then sigma ac is equal to Sigma ca. And Sigma bc

Â equals cb but therefore the 6 and the 3.

Â But this spot, if it confuses you, just ignore it for the time being.

Â Everybody's okay with 3 plus 6 is 9? How did I get nine?

Â And remember this 9 is 3 squared.

Â So, it's very important to understand how the pattern is emerging.

Â Why three squares? Three people

Â in a thing squared is 9. Three of them are what?

Â Variances, unique. Six are relationships.

Â Okay?

Â Let me go one step further before taking a

Â break, and show you the most fascinating thing ever.

Â Suppose

Â [LAUGH]

Â you have 500 assets. Who, which portfolio has 500 assets?

Â S&P 500.

Â Can you believe one day I really walked into

Â class and said, how many things are in S&P 500?

Â And, you know, I mean, rightly enough the class thought

Â I was an idiot, which wasn't a surprise to me.

Â But, anyway. So, so 500.

Â Right? How many total factors?

Â Remember, in what

Â [LAUGH]

Â ?

Â You should ask, "In what?" in the variance.

Â Total factors, 500 squared.

Â I can, I mean, it's mind boggling

Â how many, 250000. Right, there

Â should be four 0s. And five times five is 25.

Â 250,000 happening in a portfolio. Isn't it mind-boggling?

Â Why did I pick 500? Because there's simply 500 hares /g.

Â But why did I jump from three to five?

Â Because it would take two years to finish this

Â class if we went from three to four to five.

Â But the other reason I did is because portfolios already exists.

Â So why create their own?

Â And that's something I want to talk about for a second.

Â You buy mutual funds which already exist, and Vanguard

Â is one of the companies which has taken portfolio theory

Â 17:27

You are Google, you are Moogle, you are Doogle,

Â all of them in a room, 500, how many personalities?

Â 500.

Â You don't even need to do that math. Remember, weights are very important.

Â But let's assume they're roughly equally rated.

Â What is the weight going to be?

Â One over 500.

Â In other words, you're just buying

Â a portfolio, let's assume it's equally rated,

Â it may not be, right.

Â Is equally rated, you don't have to worry about how much do I put in this asset or

Â not, so you see, in some sense, now the

Â in large portfolio, the weight is not that important.

Â Right, what's more important, diversification.

Â Every spread, so don't buy 500 in Technology, buy 500 across.

Â How many relationships?

Â And this is going to blow your mind, you should know the answer.

Â 249,500.

Â [BLANK_AUDIO]

Â 249,500 relationships

Â going on in your portfolio. Why?

Â How did I get that?

Â Very easy.

Â Total relationships is squared, right here.

Â Subtract the unique, what am I left with.

Â 18:53

And you can actually do this math separately, directly, but why

Â do it when you know the answer in a simple fashion.

Â But what will those be, 1 to 2, 2 to 1, 1,3,2,3 and all of those.

Â Okay, so just think through this.

Â But, what's the bottom line? How many unique relationships?

Â 19:21

Why?

Â Because they come in pairs. So the bottom line of,

Â what we have learned right now before we take

Â a break is very quickly the bottom line, and I'll repeat this after the break.

Â Think about it. Variance of an asset, I'll quickly go

Â through this, take a break.

Â Variance of an asset determines risk faced by you.

Â Only if you hold 1 or very few.

Â 20:09

All relationships between people, or assets

Â [LAUGH]

Â , is due to common rather than specific things.

Â Let's take a break now.

Â We'll pick up with this slide.

Â I'll go through this very seriously and slowly.

Â And we will think through each one to come up, to come up with the bottom line.

Â Let's take a break.

Â See you soon, bye.

Â