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Risk and return: Introduction — Transcript

by Luke Stein · 2,303 words · 401 segments · language en · Watch on YouTube

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0:01luke stein here with a brief
0:02introduction to the math behind return
0:04and risk
0:05in finance we've said that investors
0:08look for three things to make an
0:10investment attractive one it should
0:12deliver large payouts
0:13two those payouts will hopefully come
0:15soon and three
0:17they should be relatively safe that is
0:18to say investors should be able to
0:20predict those payouts with high
0:22confidence
0:23and the investment should therefore be
0:25low risk
0:26the trade-off between the first two
0:27large payoffs and payoffs that come soon
0:30is captured in the mathematical tools we
0:32called the time value of money
0:34this short video is going to introduce a
0:36way of using those same mathematical
0:38tools
0:38or tvm tools or discounting in order to
0:41incorporate the risk and return
0:43trade-off
0:44[Music]
0:45[Applause]
0:46[Music]
0:53so discounting provided a valuable
0:55framework for valuing assets in
0:56particular through the dcf or discounted
0:58cash flow
0:59technique where a discount rate showed
1:02up in the denominator of all of those
1:04calculations
1:05we always said that the present value
1:06equaled some function of future cash
1:08flows
1:09and a discount rate and we describe that
1:11discount rate as the appropriate
1:13risk adjusted discount rate designed to
1:15capture both the fact that investors
1:17don't like waiting
1:18that is the time value of money but also
1:20the possibility that expected future
1:22payouts may not actually materialize
1:24of course the payouts may be better than
1:26expected but they might be worse
1:28and so to the degree that investors
1:30expect higher levels of risk in
1:32anticipated future payoffs
1:34we're going to introduce a higher value
1:37of the discount rate designed
1:39to capture the fact that investors
1:41require higher rates of return as
1:43compensation
1:44for risk in those future payoffs and of
1:46course since the discount rate shows up
1:48in the denominator of all of our
1:49discounting calculations
1:51that higher expected or required rate of
1:53return is
1:54also going to show up as a lower price
1:57or value
1:58for investments today that deliver
2:01riskier payoffs in the future
2:03so how's that going to work out well we
2:05know that capital providers should be
2:07willing to pay less
2:08or equivalently require higher rates of
2:09return on investments that they consider
2:11riskier
2:12and therefore there are a variety of
2:14ways that we could try to include
2:15risk in our valuation models we're going
2:18to introduce one
2:19which is that higher risk is going to
2:20show up as an elevated
2:22discount rate so by increasing the
2:24discount rate
2:25we're going to capture both um
2:27inpatients the pure time value of money
2:29and investors risk aversion that higher
2:31discount rate is going to show up as
2:33lower asset prices
2:35and higher rates of return those two
2:36things always go hand in hand
2:38if you pay less for any investment that
2:40delivers the same future payoffs
2:42by paying less you should be able to
2:44receive higher rates of return on your
2:46investment
2:47so at this point the math behind that is
2:49going to look extremely simple
2:51we're just going to say that the
2:52discount rate we use to value any
2:53financial asset
2:54should capture not only the time value
2:57of money which we'll call the risk-free
2:59rate
2:59the rate of return that an investor
3:01would require on a risk-free investment
3:03that is to say compensation
3:05for the fact that she's impatient and
3:06she would rather get paid soon rather
3:08than later
3:09but we're going to increase that
3:10discount rate by some amount called a
3:12risk premium
3:14what exactly drives that risk premium is
3:16going to depend on exactly what type
3:18of financial asset we're talking about
3:20um and so we'll have more to say
3:22specifically for bonds and for stocks
3:25for bonds the major source of risk is
3:27going to be associated with the
3:28possibility of default
3:30uh non-payment of expected or promised
3:32future payments
3:33although that's not actually going to be
3:34the only source of risk for bonds
3:36but if we think about default as being
3:38the major driver
3:40of risk for a lender or for a bondholder
3:43riskier bonds those that have higher
3:45probability of default
3:46all else equals should be associated
3:48with higher risk premia therefore
3:50higher discount rates and therefore
3:52lower bond prices
3:53and higher bond yields for stocks this
3:56is going to require a little bit more
3:58nuance
3:58and a little bit of a richer set of
4:00tools so the two key questions that
4:02we're going to need to ask in order to
4:03figure out how to apply this discounting
4:05based
4:07math behind the risk and return
4:09trade-off that is to say how much should
4:11we increase the discount rate to account
4:12for a relevant risk premium
4:14is really going to require us to answer
4:16two questions the first is
4:18how does a capital provider measure the
4:20risk associated with a given investment
4:22and then secondly how do we estimate not
4:25only the relevant risk-free rate that's
4:26going to serve as a baseline
4:28but also the risk premium that a capital
4:30provider is going to require
4:32given the way that they measured risk
4:34the answer that we gave to that first
4:35question
4:36so um just as a preview we're going to
4:39have more detail on this
4:40but let me try to describe to you how
4:42we're going to do this on the debt side
4:44and on the equity side
4:46so for debt the cost of debt and i
4:49should be clear this is the cost
4:50paid by the borrower or by the bond
4:53issuer
4:54the return that's received by
4:56bondholders or lenders is paid by the
4:59borrower or the bond issuer
5:00and so whereas on the last slide i call
5:02this the discount rate that drives
5:04uh the investor or the lender's
5:06valuation we can also think about this
5:08as the cost
5:09that's paid in order to get access to
5:11those funds by whatever company
5:13does the issue the cost of debt which on
5:17a loan is typically going to be
5:18associated with the interest rate on
5:19that loan
5:20on a bond it's going to be associated
5:22with the yield to maturity on that bond
5:23is going to come as we noted on the
5:25previous slide
5:26from the relevant risk-free rate and
5:29from a risk premium which in the course
5:31of bonds we're going to call the credit
5:33spread on those bonds
5:34on that bond so the relevant risk-free
5:36rate on a bond
5:38we'll typically think of as being what
5:40kind of rate of return
5:41a lender could get if they made a
5:44risk-free loan
5:46of the same duration so what that's
5:48going to mean is
5:49on a five-year bond we're going to look
5:50for a five-year risk-free benchmark on a
5:5210-year bond we're going to look for a
5:5410-year
5:55risk-free benchmark what about the
5:57credit spread
5:58well the credit spread is going to be
5:59the additional rate of return
6:01that bond investors require as
6:03compensation for taking on
6:04risk associated with a risky bond or a
6:07risky loan
6:08rather than a risk-free one and given
6:11the major source of risk not the only
6:13source but the major source of risk
6:14on bonds is going to be default risk the
6:18possibility of non-payment
6:20uh this risk premium is largely going to
6:21be a function of a bonds credit rating
6:24more to come about what those credit
6:25ratings are on the equity side
6:28we're going to wind up describing the
6:29relevant cost of equity
6:31as again starting with a relevant
6:33risk-free benchmark where that risk-free
6:35benchmark is going to be associated with
6:36the duration of the equity investment
6:38a little bit subtler there i know that a
6:40five-year bond is a five-year investment
6:42i know that a ten-year bond
6:43is a ten-year investment it's not really
6:45clear to me how i should think about the
6:47lifetime of an equity investment um to
6:50that we're going to add
6:52as always a risk premium where the key
6:55model that we're going to use
6:57to describe equity risk premiums is
6:59going to be a model called the capital
7:01asset pricing model or the cap m
7:02c apm model and that risk premium
7:06is going to be estimated as the product
7:08or the multiplication of two things
7:10one is going to be a measure called beta
7:13which is going to be a measure of the
7:14amount of
7:15investment specific risk in a given
7:17investment
7:18and that amount of investment specific
7:20risk is going to be measured
7:22using linear regression and is going to
7:24be based on the amount of co-movement
7:26that a given stock has with the market
7:28as a whole
7:29the second component that beta is going
7:31to multiply is something called
7:33the market risk premium so again a risk
7:35premium
7:36tells us how much extra compensation
7:38investors require
7:39in order to make a risky investment the
7:41market risk premium is going to be the
7:43risk premium
7:44on the stock market how much extra
7:46compensation
7:48does an investor require in order to
7:50hold an investment which is
7:51as risky as investing in the broad
7:53aggregate stock market
7:55and we can do that by subtracting off
7:57the risk-free
7:58benchmark rate from investors
8:01expected return on the market so we may
8:05be trying to figure out the risk premium
8:06on a given equity on a share of tesla or
8:08a share of gamestop
8:10or a share of of intel um but in order
8:13to do that we're going to try to
8:14understand
8:15what's the risk premium not only on
8:16those individual stocks but on the stock
8:18market as a whole
8:19how much do investors require as
8:21compensation to invest in
8:23the stock market collectively well we
8:26can subtract off
8:27the amount that they um could earn on a
8:30risk-free investment
8:31from what they expect to earn when they
8:32invest in the market as a whole and that
8:34difference called the market risk
8:35premium
8:36is going to tell us in a sense about the
8:38the price of risk
8:40so you can think about beta as a measure
8:41of the quantity of risk and the market
8:43risk premium
8:44as a measure of the price of risk one
8:47last thought before we dive into the
8:48specifics of data and equity
8:50um you may have noticed that a variety
8:53of terms are already looking like they
8:54have some connection to each other
8:56so i talked about the discount rate that
8:58was to say the
8:59higher rate of return that investors
9:02used when they
9:03valued an asset but then i started
9:05talking about the cost of debt and the
9:06cost of equity it turns out that
9:08under a set of common assumptions
9:10assumptions that we'll often make
9:11although they may not actually hold
9:13many conceptually distinct values turn
9:15out to be equal to each other
9:17so the discount rate is going to be the
9:19rate of return that investors use when
9:21they engage in discounting in order to
9:23um
9:23to value a financial asset and that's
9:26going to be associated of course
9:28with the price or the return that the
9:30issuer the borrower has to pay
9:32in order to convince anyone to invest in
9:35its investments
9:36to to invest in its securities well how
9:38do
9:39investors think about what discount rate
9:41to apply
9:42well one thing they might do is compare
9:45a given investment
9:46to other alternative investments that
9:49they might make and in particular other
9:50alternative investments
9:52that they might make that seem somehow
9:54similarly risky
9:55so if i didn't invest in this bond if i
9:58didn't invest in this stock
9:59what else might i do with my money and
10:01what rate of return could i earn on
10:03those investments
10:04and so in that sense the discount rate
10:05that investors apply
10:07should be their opportunity cost that is
10:09to say the rate of return that they
10:10could earn
10:11elsewhere on a similarly risky
10:13investment so if they're going to be
10:15willing to make this investment
10:17it must be that this investment delivers
10:19an expected rate of return
10:21at least as high as their opportunity
10:23cost so we know that the expected return
10:25has to be at least as high as investors
10:27opportunity cost in order to attract any
10:29investors
10:30and it turns out that as long as there
10:32are many investors competing
10:34to buy up the best possible investments
10:36there's no reason
10:37that an issuer of a security should
10:40offer
10:41an expected return higher than the
10:42opportunity cost well
10:44if the buyers of the security require
10:46that the expected return be at least as
10:48high as the opportunity cost
10:49and the issuers have a variety of
10:52potential investors just
10:53to select from and aren't going to offer
10:55a return lower than the opportunity cost
10:58than in a competitive market that
11:00expected rate of return
11:01should exactly equal the opportunity
11:03cost or required rate of return
11:06that investors apply so we often wind up
11:08also calling this investors required
11:10rate of return
11:11i'm going to require that this
11:12investment offer a return as
11:15good as my best alternative or
11:16opportunity costs um and once we
11:18introduce capital budgeting
11:20you'll see that we're also going to
11:21associate this discount rate with a
11:23concept called the hurdle rate
11:25um and that has to do with the fact that
11:27when a firm raises funds by issuing
11:29financial security say by borrowing by
11:31selling
11:32stocks by selling bonds it's
11:35only going to want to do that if it can
11:38find
11:38projects to invest in that deliver
11:41returns at least as high
11:42as that discount rate and so on the
11:45capital provision side
11:47um the discount rate is going to be
11:48associated um with the rate that
11:50investors
11:51charge demand or require um from the
11:53firm but the firm is then going to
11:56make sure that it has opportunities to
11:58grow those funds in the course of its
12:00business
12:01by investing in projects that can
12:02deliver returns that
12:04are at least that high
12:12foreign

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