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Hi, welcome back to finance for non-finance professionals.

This week we're talking about the cost of capital or what discount rate to use.

In this lesson, we're going to talk about company betas and their cost of equity,

and we're going to figure out how to calculate an actual cost of equity for

individual firms.

Okay, if you remember back to our lesson on stock riskiness,

the equity premium we said was around 5.5%,

that compensated us for putting our money in the stock market overall.

But what if I put my money in one single stock, what if I put my money in one share

of Google, or one share of Chevron, or one share of IBM?

What kind of a return should I expect for putting my money in a single stock?

Well that seems riskier potentially than putting my money in the stock

market overall.

So what would the premium for that be?

How should I measure how risky and individual stock is?

If the overall stock market should return 5.5%, how much

extra risk premium should I get for putting my money in one specific stock?

And how would I measure how risky that stock is?

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It wiggles a lot, right?

That's probably my most sort of intuitive measure is that it just moves

around a lot.

I never know what's going to happen to it.

Maybe it jumps around too much, or one day it's up 10% and then goes down 30%.

How has it done in the past, has it been going up over time,

does that reduce the risk?

Has it been going down over time?

Those are all what we call stock specific risks.

If I look at that one stock I can see that one stock wiggles around a lot, or

that one stock has big jumps up and down.

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Okay, but I don't have to buy one specific stock,

I could buy lots of different stocks.

And as I buy lots of different stocks that diversification might reduce my risk.

In other words, if I had required 20% to hold a stock that risky, but

some other investor says, well, I'm not going to charge you 20% extra return,

because I'm going to put you in a diversified portfolio.

The company's going to raise money from that investor.

So we have to think about diversification and

how that diversification sort of plays into the risk of individual stock.

Let's put this through and example.

I've got a graphic here where I'm showing you the historical returns for

the roughly five years on three stocks, IBM, General Electric, and Apple.

Apple is the purple line that goes up the most and

you can see that line goes up at around 21% a year, plus or

minus 27%, that's a lot of volatility.

General Electric is the red line that kind of cuts the middle and

that one goes up on average 15% a year over five years, plus or

minus around 19%, wiggles a little bit less.

And then IBM is the blue line that's done kind of meh over the last five years,

kind of hasn't had great returns, but

has gone up on average 5% over the last five years, plus or minus around 17%.

So you could say okay, well I should charge Apple sort of the most, I should

charge GE, in terms of risk premium, the middle, and charge IBM the lowest.

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But what if I put all three into a diversify portfolio

together on average what would I charge that for portfolio.

If I did that, that's that black line that I have got now cutting through

the shadow of those three lines, that's a much smoother line.

That line goes up at around 14% plus or

minus only 12% that's the smoothest of any of those lines.

In other words, putting those together into one portfolio, those wiggles,

those little, I think of stock chart is like little butterfly wings, yeah?

As they kind of fly through time

the back of their wings sort of leaves a trail of stock returns.

As I put those in to a portfolio, those butterfly flaps cancel each other out.

Like the versivacation, sometimes AAPL goes up a lot when IBM goes down.

Sometimes GE goes up when IBM and Apple go down, and

those cancellation of each other's variation smooth out that line.

From an investors perspective, that's what I'd love.

I would love to just sit back and smoothly earn 5.5, 6,

7%, and not have to worry about the ups and downs of the market.

The more I diversify, the more comfortable I can get about putting my money

into risky securities like stocks because those variations cancel each other out.

The more I can get those variations to cancel each other out,

the more comfortable I feel, the lower the return I'm going to require for

an individual stock.

So what we want is a measure of how each stock makes that black line,

that portfolio line, wiggle.

If I put that stock in my portfolio,

does it make that portfolio line wiggle more or wiggle less.

Now it's going to depend not really on how much that stock wiggles, but

how it wiggles with the other stocks in my portfolio.

That's a key concept that I want you to get from this lesson.

The risk of a stock is coming not just from how much it wiggles around, but

how much it wiggles with the other stocks in my portfolio.

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That means, holding multiple stocks can reduce my risk.

Why not hold lots of stocks, why not hold the whole market?

What we're going to think about is how to measure the risk of an individual stock.

Wiggles and jumps might be good if that stock wiggles and

jumps independently of all the other stocks in my portfolio.

So what we want to measure is, how does the stock change the risk of my portfolio?

How does the stock make my portfolio wiggle more or less?

That's going to get us to our measure of beta.

Now beta is going to tell me how much the stock wiggles with the market.

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about the covariance, how two things wiggle together.

If two little butterflies are flying and

they tend to move together, they've got high covariance.

If two little butterflies are flying, but they fly as sort of independently, they

don't matter to each other, then there's sort of no covariance between them.

They more they fly together, the more in love they are,

the more covariance there is, the more they wiggle together.

Covariance is the physical measure of how things move together, variance,

a measure of how things move overall.

That's about as technical as we need to get, the beta measure that we're going to

use for an individual stock's risk is a ratio of those two things.

How much does my stock, the stock that I'm looking at, move with the market.

And that's what we've got down here what we're calling the covariance between our

i, my stock and the market, Rm.

That's the covariance term,

that's the numerator, how much do I move overall with the market?

And then I'm just going to take that measure covariance and

scale it through by how much market moves overall.

We're going to call that measure, that ratio wiggling, how much I wiggle with

other things, divided by how much the market wiggles overall.

We're going to call that a stock beta, and

that's going to be a measure of how much I move with the market.

If I put that stock into my portfolio,

does that make my portfolio wiggle a lot or does it make it wiggle less?

That beta is a measure of how risky my stock is in a portfolio.

Betas are usually around one.

They can go as low as around 0.25 and sometimes as high as 2.5,

but they're usually most almost all betas are somewhere in that range.

And that beta tells me how much market risk I'm taking when I buy that stock.

For example if a stock has a beta of two,

that stock wiggles twice as much as the market.

So if we remember what a market risk was, market risk goes around 5.5%,

I would require two servings of market premium in order to buy that stock,

because that stock is twice as risky as the market return.

Okay, two servings of market risk should have much higher returns.

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When we think about the cost of equity,

that rate of return was the risk free rate plus some risk premium.

We've now got a way to think about what that risk premium is.

That risk premium should be beta, how much market risk I'm taking,

times the equity premium, the 5.5% which is one serving of market risk.

Beta is sort of how many servings of market risk I need and

the equity premium is one serving of market risk.

We can put that together now In finance what we call the CAPM the capital asset

pricing model, which tells the risk of return of any asset

is the risk free rate plus beta times the Equity Premium.

And that's simple formula gives me a formula for putting on a risk on

any stock because every stocks going to have a different beta.

If I calculate that beta or just look it up on Yahoo.

I can say that the return on that stock ought to be what I expect, what I should

use to discount equity is the risk free rate plus beta times the equity premium.

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So for example, if a stock has a beta 1.8 and the risk premium and

the equity premium is around 5.5%, the risk-free rate is 3%,

how would I calculate the cost of equity for that stock?

It would be the risk-free rate, plus beta, times the equity premium.

In this case, that would be 3% + 1.8 x the 5.5% equity premium, 12.9%.

Now I've got a number, now I've got a discount rate that I can use to discount

what, I think, are going to be future cash flows to the equity holders.

Another way to think about that is if I buy that stock,

how much do I expect to earn for taking that much risk?

I expect to earn about 13% for a stock with a beta of around 1.8.

Okay, if we go back to that simple balance sheet when we started this week we said

there was stuff on the left hand side.

And we said there was debt, and

there was equity, well now we've got a way to discount the cashflows to equity.

That's going to be our capital asset pricing model,

the risk free rate plus beta, times the market premium.

In the next lecturers we're going to talk about what discount rate to use for debt.

So diversification changes risk,

market risk can't be diversified away; that was that 5.5%.

Beta measures our sensitivity to that market risk, and when we put those two

things together, risk-free rate plus beta times the equity premium,

we've got a way to discount the risk of owning individual stocks.