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

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

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

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

Â individual firms.

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

Â the equity premium we said was around 5.5%,

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

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

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

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

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

Â market overall.

Â So what would the premium for that be?

Â How should I measure how risky and individual stock is?

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

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

Â And how would I measure how risky that stock is?

Â 1:07

It wiggles a lot, right?

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

Â around a lot.

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

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

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

Â does that reduce the risk?

Â Has it been going down over time?

Â Those are all what we call stock specific risks.

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

Â that one stock has big jumps up and down.

Â 1:34

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

Â I could buy lots of different stocks.

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

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

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

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

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

Â So we have to think about diversification and

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

Â Let's put this through and example.

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

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

Â Apple is the purple line that goes up the most and

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

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

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

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

Â minus around 19%, wiggles a little bit less.

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

Â kind of hasn't had great returns, but

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

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

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

Â 3:07

But what if I put all three into a diversify portfolio

Â together on average what would I charge that for portfolio.

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

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

Â That line goes up at around 14% plus or

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

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

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

Â As they kind of fly through time

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

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

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

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

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

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

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

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

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

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

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

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

Â an individual stock.

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

Â that portfolio line, wiggle.

Â If I put that stock in my portfolio,

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

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

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

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

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

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

Â 5:06

That means, holding multiple stocks can reduce my risk.

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

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

Â Wiggles and jumps might be good if that stock wiggles and

Â jumps independently of all the other stocks in my portfolio.

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

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

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

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

Â 5:46

about the covariance, how two things wiggle together.

Â If two little butterflies are flying and

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

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

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

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

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

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

Â a measure of how things move overall.

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

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

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

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

Â i, my stock and the market, Rm.

Â That's the covariance term,

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

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

Â scale it through by how much market moves overall.

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

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

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

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

Â If I put that stock into my portfolio,

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

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

Â Betas are usually around one.

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

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

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

Â For example if a stock has a beta of two,

Â that stock wiggles twice as much as the market.

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

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

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

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

Â 7:52

When we think about the cost of equity,

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

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

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

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

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

Â the equity premium is one serving of market risk.

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

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

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

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

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

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

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

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

Â 8:45

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

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

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

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

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

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

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

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

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

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

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

Â there was stuff on the left hand side.

Â And we said there was debt, and

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

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

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

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

Â So diversification changes risk,

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

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

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

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

Â