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Finance Lecture - Risk, Return and CAPM — Transcript

by Brad Simon · 5,494 words · 869 segments · language en · Watch on YouTube

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0:01hi everybody and welcome to our next
0:03Finance lecture this lecture focuses on
0:05risk return and the capital asset
0:08pricing
0:10model just a quick overview of what
0:13we'll be talking about I first want to
0:14just introduce the concept of risk and
0:17return and and then we'll take a first
0:19uh we'll talk about calculating returns
0:21and we'll take a First Step at measuring
0:24risk um we'll then explore ways that we
0:27can reduce risk through diversification
0:30which will then lead to another take on
0:33how to measure risk with our updated
0:35diversification ideas and then finally
0:39this will lead to the creation of the
0:41capital asset pricing model and uh a way
0:45that we can estimate how to price risk
0:49and then we'll wrap up the
0:52lecture all right so let me motivate the
0:54topic of risk and return so first of all
0:57the relationship between risk and return
0:59is a fun fundamental piece of Finance
1:02Theory as an example this is a very
1:04simple example if given a choice between
1:06investing in a low risk opportunity that
1:09says it's it's going to probably pay you
1:1310% uh return on your money or investing
1:17in a high-risk opportunity that says
1:19it's going to pay you 10% well we're not
1:22sure that we're going to get the 10% uh
1:25so which of these two would you choose
1:28well most people would choose the the
1:30lower risk opportunity if you have a
1:32choice of making 10% with a lowrisk
1:34situation or maybe there's a risky one
1:38generally we're going to go for the
1:39lower
1:41risk so this principle is something that
1:44we follow in in finance which is that
1:46investors need the inducement of higher
1:49reward to take on perceived higher risks
1:53and this is this is an axium that flows
1:55through finance and we're going to
1:57develop that in this lecture
2:00let's start by defining what a return on
2:02investment is and what we mean by that
2:05so we can invest in a stock with the
2:07hope of earning a positive return on our
2:10investment right we want to make some
2:11money on it otherwise we wouldn't
2:14invest well we need a way to measure
2:16this
2:17return for stocks we have two components
2:21that can contribute to our return we can
2:25receive a dividend
2:26payments or the stock price itself can
2:31appreciate all right so let's work with
2:34these two things so just a recap stocks
2:37have two returns components dividends
2:39and stock price appreciation and we can
2:42express this in an equation as follows
2:45the percentage return is equal to the
2:49ending price of the stock minus the
2:51beginning divided by the
2:54beginning plus the dividend divided by
2:57the beginning price and
3:00the first term deals with the stock
3:03price appreciation and the second term
3:05deals with the
3:07dividend and we can actually we give
3:09those names the percentage return is
3:11equal to the capital gains yield that's
3:14the stock price appreciation plus the
3:17dividend yield the return we get from
3:19the
3:20dividend and this allows us to measure
3:23the return on a stocks on our investment
3:27from a
3:28stock
3:32so for example assume that we purchase
3:35one share of a stock at $25 and received
3:38$2 in dividends during the year after
3:41one year the stock price increased to
3:44$31 what is the percentage return that
3:47we
3:48achieved well let's just do the math we
3:51take our percentage return it equals the
3:53capital gains yield plus the dividend
3:55yield and now we can just plug in the
3:57numbers 31 - 25 ID 25+ 2 / 25 right I'm
4:03just putting in the values from above
4:05into this
4:07equation and that it's reduced to the
4:10capital gains yield is 24% and the
4:13dividend yield is
4:168% which is a total return of
4:2032% which that's not
4:23bad uh at least that looks pretty
4:26good um but regardless that's how we
4:29calculate it
4:32it so now I said that it looked pretty
4:35good right well let's talk about that a
4:37little more the previous example
4:39calculated what actually happened in
4:41this hypothetical situation and we can
4:43call that a historic return this is you
4:47know it's it's it's history it happened
4:51um however prior to making the
4:53investment we may have had an expected
4:56return of let's say
4:5850% and we didn't get
5:0250%
5:03so in this case what actually happened
5:06was we we fell short of our
5:09expectations so that's not
5:12good um
5:14alternatively maybe our expectations
5:16were to earn only 10% and in that case
5:20we exceeded our
5:21expectations right so we earned 34%
5:24return and uh if we had expected
5:27something higher then we fell short if
5:30we expected something less then we did
5:32well so that that kind of gives us a
5:35hint of how we're going with uh with
5:38risk how this relates to measuring up to
5:41our
5:43expectations so now let's let's use
5:45these Concepts to to help us Define
5:48risk so the the fact that what actually
5:52happens May and really often does differ
5:54from what we either expect or would like
5:57to happen we can Define as
6:01risk so not we're especially sensitive
6:04to risks related to underperforming our
6:07expectation right if we're above our
6:10expectation uh we're actually pretty
6:12happy with that but we are really not
6:15happy when we fall below our
6:21expectations so now it's useful to have
6:23a mathematical tool so that we can
6:25measure our concept of risk we're in
6:28finance like math so we have tools for
6:32these things a common approach is to
6:34look at a distribution of either the
6:37historic or the projected returns and
6:40calculate the volatility which is either
6:42the standard deviation or the variance
6:44typically of the
6:47returns so the following slide shows two
6:50different distributions superimposed and
6:53I'll just talk about what they mean when
6:55we see the
6:58slide
7:01uh so here we have the probability
7:04distributions of returns for two stocks
7:07and B and question is is one question is
7:12which stock is riskier so let me just
7:15explain this for a second you can see on
7:17the on the horizontal axis we've got our
7:21returns zero is over to the left here
7:23the average which both of these pass
7:25through is 15% so that's a 15% return on
7:29the stock
7:30right in the previous example it was a
7:3234% return so that's what we're we're
7:35looking at here it's a 15% return and
7:38then you can see these distributions so
7:41we have under the red one the likelihood
7:45of Landing somewhere close to the
7:49average uh it's it's greater than the
7:51green
7:52one it is clustered more closely to the
7:56mean it's less dispersed
8:00so we can say that stock a our red
8:05distribution here is less risky than
8:08Stock B and the reason for that is
8:11because we have a greater chance of
8:13being further below what we
8:16expected with Stock B by just looking at
8:20this now we also have a greater chance
8:22of being higher than what we expected
8:27but we're more risk averse
8:30uh and that will guide us we actually
8:33are we we we do not like to be below our
8:39expectations so we say that Stock B is
8:43riskier again because there's a greater
8:46likelihood that we will be further away
8:49further below our expectations than
8:52stock a
8:58returns
9:00so now just to recap this both stocks
9:03have the same average they are both at
9:0615% and the returns for stock a are more
9:10tightly clustered around the average
9:12than those of Stock
9:15B so if we assume the average of 15% was
9:19our expected or required return then we
9:21consider stock a to be less risky as it
9:24does not stray as far from our expected
9:27return value and and more importantly is
9:31our preference to avoid bigger and bad
9:35surprises so while both stocks A and B
9:37have an equal chance of falling below
9:39our expectations or above Stock B will
9:43likely Fall further from our expected
9:46return than stock a so because we're
9:49extra sensitive to lower performance we
9:52conclude the following the larger the
9:55volatility the bigger the standard
9:57deviation of the variance the greater
9:59the risk and that's our first takeaway
10:02for measuring
10:05risk through this volatility
10:08metric the greater the volatility the
10:11greater the risk all right now let's do
10:14a mathematical example of
10:16this a quick reminder of the formulas
10:19for variance and standard
10:22deviation Sigma is the representation
10:25for standard
10:27deviation and the variance is just Sigma
10:32squared the standard deviation formula
10:35is this thing in front of you the square
10:38root of the sum of the return of a given
10:40stock minus the average divided by
10:43squared divided by n minus one for a
10:47sample
10:51population okay so let's go ahead and
10:53calculate the
10:55volatility so example use the following
10:58returns calculate the average return the
11:00variance and the standard deviation for
11:03Acme stock so here are some returns in
11:07year one there was a 10% positive return
11:10in year two a 4% return in year three
11:13negative 8% there was a loss and so on
11:16for five
11:18years all right so now let's actually
11:22crunch the numbers here we the first
11:24thing we need is to calculate the
11:26average return which is just we add up
11:28all the returns from the previous slide
11:31and we divide by five the number of
11:33returns we get 4.8% so on
11:36average the these add up we received a
11:39return of
11:404.8% and now we want to know well how
11:44dispersed were those returns we can
11:47start with the variance formula and
11:50we're just going to plug our numbers in
11:52there we start with 10 we minus the
11:54average we Square it and then we do this
11:57for each of our actual returns and you
12:01get about 65% you take the square root
12:04of that and you get 8% I'm just you know
12:07crunching some numbers here the
12:09conclusion from this is the greater the
12:11standard deviation the further we are
12:14away from our average return and when
12:17we're on the left side of that curve uh
12:21that is just
12:23amplifying that we're in an even worse
12:26position because we're we're we're
12:28falling short of our expectation by even
12:30more the greater the standard
12:38deviation so now this is I want to just
12:41show a chart of the volatility of stocks
12:44and bonds over some historic
12:48periods and the idea is that the
12:50volatility of stocks is much greater
12:53than the volatility of bonds and
12:56treasury
12:58bills
12:59so just to look at the the the Top Line
13:02it's from some standard deviations of
13:05Returns on stocks and treasury bonds uh
13:09over let's say from 1950 through right
13:12up to the recession in 2007 just before
13:15it and you can see the returns for
13:17stocks are 177% on average and the
13:20returns for treasury bonds 10.3 and for
13:24treasury bills much shorter term
13:26instruments uh
13:282.8% so you can see as we would expect
13:32stocks are riskier than government
13:34issued bonds which are even riskier than
13:37shorter term governmen issued treasury
13:39bills and as risk in as the risk
13:42component increases uh so does this
13:45return which is intuitive and then uh
13:49you know you can see by different
13:52decades these the returns have different
13:55calculations so it does fluctuate over
13:58time but the main takeaway from this is
14:01you can calculate these over longer
14:03periods of time and you can see that uh
14:06there are different types of assets that
14:09have different uh
14:11risk uh risk
14:19factors so now let's just talk a little
14:21bit about
14:23um diversifying risk so in the beginning
14:26of the lecture we saw that higher risks
14:29must come with at least the potential
14:31for higher returns otherwise the
14:33investor just simply won't put their
14:34money
14:35there we also saw that more volatile
14:39stocks should have on average higher
14:42returns right the riskier a stock is the
14:45more the investor is going to need to
14:48be promised for a return in order to
14:51invest in
14:54that now we can actually reduce the
14:58volatility we use the standard deviation
15:00right but we can actually reduce the
15:03volatility for a given level of Return
15:05by grouping assets into
15:08portfolios this is known as diversifying
15:13risk all right so let's go through an
15:15example of how this works with
15:19diversifying risk and
15:21portfolios and uh let's let's just say
15:23we're interested in purchasing uh a
15:26pharmaceutical company stock
15:29now in a given year a particular
15:32pharmaceutical company May Fail in
15:34getting approval of a new drug and that
15:37would probably cause its stock price to
15:40drop but it's unlikely that every
15:43pharmaceutical company will fail major
15:45drug trials in the same
15:48year on average some are likely to be
15:50successful While others will
15:53fail therefore the returns of a
15:55portfolio comprised of all drug
15:58companies will have much less volatility
16:00than that of a single Drug Company in
16:04other words it might be better for us to
16:07invest in a portfolio of drug companies
16:10if we're interested in the
16:11pharmaceutical sector rather than just
16:13pick
16:18one all right let's continue this so now
16:21by holding the entire sector of
16:23pharmaceuticals we've eliminated quite a
16:25bit of
16:26risk but it's possible there's still
16:28sector level risk that may impact all of
16:31the drug companies for example if the
16:34FDA changes its drug Approval Pro policy
16:38and requires all new drugs to go through
16:40more strict testing we would expect the
16:43entire sector and our portfolio comprise
16:46of all the Pharmaceuticals to
16:50suffer so now but what if we held a
16:54portfolio of not just pharmaceutical
16:56companies but also of computer companies
16:59manufacturing companies service
17:00companies and maybe even real estate or
17:02Commodities and other
17:06assets well we would expect this
17:08expanded portfolio to be even less risky
17:11than a portfolio comprised of just one
17:14sector in fact we can imagine a market
17:16level portfolio comprised of all
17:21assets such a market portfolio would
17:23still have
17:25uncertainty but risk uh uncertainty and
17:28risk but it would be greatly reduced
17:31compared to just one asset or holding
17:33just one asset or holding even just a
17:36group of related
17:40assets so from this discussion we can
17:42think of having risk is having two
17:46components first we can think of them as
17:49having firm specific risk or asset
17:51specific
17:53risk and then secondly there's Market
17:55level
17:57risk
17:59all right let me explain these so firm
18:01specific risk is what we saw which can
18:04be Diversified away if we holds
18:07something in a portfolio Market level
18:10risk is the stuff that's left over it
18:13just can't be eliminated we just we're
18:15stuck with
18:16it all right let me just take a moment
18:18to talk about the the naming conventions
18:21that are used
18:22here firm specific risk you'll also
18:26you'll hear it called any of the
18:28following
18:29asset specific risk diversifiable risk
18:32idiosyncratic risk and unsystematic risk
18:36so these are all interchangeable terms
18:38for firm specific
18:40risk Market level risk is also called by
18:44a number of
18:45names sis uh systematic risk Market risk
18:50and non-diversifiable risk so these
18:54are you you'll hear any of these names
18:58uh used in in
19:01finance so if you hear me use one or the
19:03other uh you know this is what I am
19:05referring
19:08to I want to just show a visual of what
19:12happens with diversification I've got
19:15two similar graphs uh just to make the
19:18point across so in this in this graph on
19:22the on the hor on the vertical axis we
19:26have the standard deviation of of our
19:29portfolio uh we have uh you know this is
19:32this is representative of risk and over
19:35here we have essentially it's the number
19:37of stocks in our portfolio
19:41and this line you can see it's the blue
19:45line starts out fairly High when there's
19:48just
19:49one stock in the portfolio in this case
19:51it's Radio Shack uh and then as we add
19:54more stock our standard deviation of the
19:57portfolio
20:00lowers and as we add more stocks and
20:03more stocks you can see it's it's
20:07approaching its the best case scenario
20:11uh which is in this graph a little bit
20:13above
20:1515% and we that's when we've added all
20:19500 stocks in the S&P 500 so we're not
20:22really going to do a lot better than
20:23this by adding more stocks you can this
20:26graph shows a couple of things one as
20:28you add stocks the benefits acre very
20:32quickly and then beyond a certain number
20:34you you get improvements but the gains
20:37are much
20:39smaller the other thing that this graph
20:41shows
20:43is this green area which is the best we
20:46can
20:47do uh is eliminate to the top of this
20:50green area and this green area is what
20:52we call the Market level risk that's
20:54just the stuff that's economy-wide stuff
20:57that is macroeconomic and companies
21:00can't control or consumer
21:03preferences uh and companies cannot
21:06control
21:07this and then the stuff that companies
21:10have a little more control over is the
21:13stuff between the the green area the the
21:17top of the market risk and the blue
21:21line so this is firm specific and this
21:24is Market
21:27specific I wanted to show another
21:29version it's a very similar graph but
21:31it's got a little less uh doesn't have
21:33all the bright colors on it and it's got
21:36a couple of the other names in there so
21:39this is a little bit more generic we
21:42have portfolio risk on the Y AIS number
21:44of Securities on the x-axis here and you
21:47can see underneath the horizontal line
21:50we've got systematic or non-
21:52diversifiable risk and this underneath
21:55the curve is the unsystematic or
21:58diversifiable risk right so as we add
22:01more stocks to our portfolio the overall
22:03risk
22:05decreases and that's uh that's the
22:07benefit of having this
22:14portfolio all right I just want to show
22:16one more graph that helps communicate
22:19what's going on here with the benefit of
22:22portfolio diversification and red and
22:24reducing
22:25risks so as we include more stock in the
22:28portfolio the volatility of the returns
22:31lessens right we are reducing
22:34risk in this graph this is similar to
22:37the earlier graph that we had seen
22:38except in that earlier one we
22:42had two different stocks in this case we
22:46have
22:47portfolios with different numbers of
22:50stocks and you can see that as we add
22:54more stocks to our
22:56portfolio the
22:59the dispersion the distance from our
23:02average gets less and we've defined that
23:06earlier as less risky right the the more
23:11closely clustered around the average the
23:14less risky our returns
23:17are um so you can see this this
23:19demonstrates that this principle that
23:22the more stocks you put in a
23:24portfolio the less risk there is
23:29in terms of falling below our return
23:37expectation how does diversification
23:40work well diversification comes when
23:43stocks are subject to different kinds of
23:45events such that the returns differ over
23:48time so for example the stocks returns
23:51are not perfectly
23:53correlated we saw that with the
23:55Pharmaceuticals maybe some get approval
23:58and some don't so their stocks are not
24:00moving they're moving in different
24:02directions at the uh at the same time
24:04period so they tend to counteract each
24:10other so by contrast if two stocks are
24:13perfectly positively correlated
24:16diversification has no effect on risk
24:18right it doesn't matter if we had 100
24:20stocks in the portfolio and every single
24:23one of them moved in perfect harmony
24:25with each other then we may as well just
24:28get rid of 99 of them there's no benefit
24:30to diversification so the real key
24:33ingredient is to have um this not
24:39perfect correlation to have some less
24:42than perfect correlations among the
24:45assets held in the
24:50portfolio all right some conclusions to
24:53diversification investors are only
24:56compensated for risks that they Bear
24:59right so we know investors need to be
25:01compensated for risks for taking on
25:03risks but really they're only going to
25:05be compensated for RI for the risks that
25:07they
25:08bear and if a risk can be Diversified
25:12away well they're not going to be
25:13compensated for it so in an in a in a
25:16competitive in an efficient market the
25:18only risks that are going to be
25:20compensated are the non-diversifiable
25:24risks right the stuff that's left over
25:27after you've been
25:29after you fully Diversified the risks
25:33away so now with that in
25:36mind um earlier we measured the risk of
25:40the return on an investment by using the
25:42standard deviation or the
25:46volatility now after our examination of
25:50this diversification concept we can see
25:52that the standard deviation measures
25:54something that we can call the total
25:55risk it measures it both diversifiable
25:59and non-diversifiable risk so it it
26:01really it captures more than we
26:05want we really we don't want to capture
26:09the diversifiable risk in our risk
26:12measurement so it it would be preferable
26:14to have a measure of the
26:16non-diversifiable risk only because in
26:19an efficient market only this kind of
26:21risk is going to be
26:26rewarded in finance we def find such a
26:29measure of non-diversifiable risk as
26:33beta so for example for stock I of our
26:39portfolio the beta is going to be
26:42defined
26:43as the ratio of the standard deviation
26:47of the stock to the standard deviation
26:49of the market as a
26:51whole
26:53times the correlation of these items so
26:59we scale the ratio of their standard
27:02deviations by how much they're
27:04correlated and if we just break this
27:06apart a little bit what this is saying
27:09is
27:10is the greater the standard deviation of
27:14the stock
27:15itself the greater the
27:19beta the greater the correlation the
27:22greater the beta and this is intuitive
27:25because we know well standard deviation
27:27does measure
27:29risk
27:30and so the greater it is we want to
27:33capture that um but now
27:36if if the stock has let's say a low
27:40correlation then we want to take away
27:42some of that risk and that's what that
27:43would be doing so the lower the
27:46correlation we actually scale back some
27:48of the impacts of the risk the greater
27:52the correlation we want to amplify the
27:57risks
28:00so conceptually what does this thing
28:03measure it measures two things a Stock's
28:07volatility relative to the portfolio as
28:10a
28:11whole right so just how much it moves
28:15relative to the
28:17portfolio and it also measures a Stock's
28:21contribution of the risk to the
28:23portfolio so the portfolio has its own
28:27risk measurement and this is the amount
28:28of risk that's contributed to the
28:30portfolio by this particular
28:36stock so again beta is telling us the
28:41non- diversifi component of risk we saw
28:45just to recap we saw that standard
28:47deviation it does measure risk but it
28:50captures both diversifiable and non
28:54diversifiable risk it captures total
28:56risk we only want the diversifi uh we we
29:00only want really to focus on the
29:01non-diversifiable stuff the stuff that
29:03we're stuck with and that's what beta is
29:07trying to
29:13capture so we define beta in such a way
29:16that a stock with a beta of one has
29:20roughly the same volatility as the
29:22market as a whole it moves pretty much
29:24with the market the market goes up the
29:26stock moves up by the same amount and
29:29likewise if it goes
29:31down betas with a that are greater than
29:34one they have greater volatility than
29:37the market so if the stock goes up by a
29:39little beta goes up by a little
29:45more and
29:47likewise with a beta of less than one
29:50it's a little less volatile than the
29:52market when the when the stock goes when
29:55the stock market goes up by a certain
29:57amount uh beta less than one will go up
30:00by a little
30:04less so now most stocks actually have
30:06beta somewhere in the range of 0.5 to
30:121.5 all right you could theoretically
30:16could you have a negative beta that
30:18means when the stock market goes goes up
30:21the beta of goes down and when the stock
30:24market goes down the beta goes up this
30:27in theory you can some people I guess
30:29you know gold can do this it can be a
30:31counterbalance in uh in in bad times and
30:35uh a little bit of a a drag in good
30:38times but in general for for most
30:44companies their their betas are positive
30:47they they move with the
30:51market here's a chart of betas for a
30:55number of companies and and you can see
30:58on this most of them are in that range
31:01that I was talking about right so 3M is
31:04a little less risky than the market with
31:06a beta of
31:0775 Alcoa has much higher higher
31:13risk and so on Walmart there we go
31:16that's almost zero so it's very low
31:24risk its returns are very stable
31:32now what are we going to do with all
31:34this stuff well we're going to use this
31:35to help us calculate what we should
31:41require to be compensated for holding
31:44these stocks that's what we're building
31:50towards
31:52so before we get to that let me just
31:54talk about one last thing on the betas
31:57um how do we even estimate these betas
32:00right I gave them to you well the
32:02reality is is there are many services
32:05that that calculate betas and and you
32:09can find some are free some are paid for
32:12um these are a list of some of them and
32:15you can just look them up for a given
32:18company if you're really being
32:20adventurous and uh wanted to slog
32:23through some some analysis you could
32:25calculate them for yourself you could
32:26get historical data and really crunch
32:29some
32:32numbers all right so we'll come back to
32:34Beta
32:37shortly let's talk about the risk
32:40premium let me introduce this concept
32:43here we started our lecture stating that
32:46we need to be induced to take on extra
32:48risk with the promise of extra
32:53return now we can think of this extra
32:56risk as being a risk premium that we
32:59require relative to a less risky
33:04opportunity so for example if our choice
33:07is between investing in a risk-free
33:09asset such as the US treasury bond and a
33:12risky asset such as a company stock our
33:16required return can be stated as follows
33:19the required return equals the risk free
33:22rate plus some risk premium some
33:26additional payment
33:32we can think of the risk premium as the
33:34reward that investors require for taking
33:37on the risk of investing in the stock
33:40and forgoing this risk-free
33:44investment again the market doesn't
33:47reward all risks right it only
33:52rewards non-diversifiable
33:55risks so since the firm spe specific
33:58portion of risk can be Diversified away
34:01an efficient market will not reward
34:03investors for taking this component of
34:10risk the market rewards only the
34:13remaining risk after the firm specific
34:15risk has been Diversified away the
34:17market
34:19risk so the market level of risk is
34:23exactly what beta
34:26calculates
34:32all right now we can move to a general
34:36model that helps us determine what we
34:39need to be compensated for taking on
34:43risk we can combine all of our prior
34:47discussions of beta and risk premium and
34:49create a general pricing Theory so the
34:52most famous of these is the capital
34:54asset pricing model or simply the capm
34:58and the capm states the
35:01following the required return on stock I
35:05this is a portfolio so it's the I stock
35:09of the portfolio is equal to the
35:11risk-free rate plus the market risk
35:16premium Times stock eyes beta
35:22coefficient all right so this is the
35:24required return for holding a stock for
35:27investing in a stock is this risk-free
35:30rate plus plus a
35:33premium right plus a market risk premium
35:37times uh the the beta of the stock
35:42itself in symbols we write it like this
35:46the return of the ice stock is equal to
35:49the risk free
35:50rates plus the beta of the stock times
35:56the risk premium of the market
35:59so the risk-free rate well we know we
36:02can look that up you can calculate the
36:04yield on a stock uh you can calculate
36:07the yield on on us bonds uh beta well we
36:12can look that up we just talked about
36:13that and the risk premium well you can
36:15look that up also there are people that
36:17calculate that as well and uh and this
36:20is at the market level so you can
36:22imagine the S&P
36:24500 has a certain risk premium if you
36:28just for holding that
36:32portfolio we can generalize this a
36:34little we can split this Market risk
36:38premium into a market return and
36:41subtract the risk-free
36:43rate so sometimes you're told the market
36:46risk premium number and sometimes you're
36:49told the market return number and then
36:51you got to subtract out the risk-free
36:53rate but either way
36:55conceptually we're taking the risk-free
36:58rate then we add the return for the
37:02portfolio itself and then we scale it by
37:05the the stocks beta that we're
37:07interested
37:09in all right so let's do an example of
37:11this right so the the capm equation
37:14tells us allows us to estimate any
37:16stocks required return once we've
37:19determined the stocks beta risk-free
37:20rate and Market risk
37:22premium so let's say we have uh we
37:25expect the market portfolio to earn 12%
37:29and treasury bonds yields uh bond yields
37:32are at
37:333.5% if the if Home Depot has a beta of
37:371.08 we can calculate the required
37:40return for holding that stock as
37:44follows the required return for Home
37:46Depot equals the risk-free rate plus the
37:49beta for Home Depot times the market
37:53risk
37:55premium let's fill in the numbers and we
37:59have the risk free rate is 3 and 1.2%
38:02plus beta is 1.08 times well we have to
38:07take the market portfolio return and
38:11subtract the risk-free rate that's our
38:13premium at the market level so it's 12
38:16minus
38:1735% and when you reduce that it's 12
38:20point it's roughly
38:2212.7%
38:24so we would need a required return of
38:3012.7% in order to put our money into
38:34Home
38:35Depot based on our view of how risky it
38:41is and we could do this with any stock
38:44and some stocks which have lower
38:47non-diversifiable risk uh those that
38:50have lower non- diversifi risk than H
38:52Depot will require less for us to uh
38:56less of a return and those that we feel
38:59uh that we have calculated to be more
39:02risky for its non- diversifiable
39:06component we would require a greater
39:14return all right some caveats on
39:17this so measures of beta for a given
39:20asset can vary depending on how it's
39:22calculated so you know we think it's
39:25this precise number but you know if if
39:27you do the math or I do the math or a
39:30third person does the math well we might
39:33all get three different numbers
39:34depending
39:35on the data that we're using or how far
39:38back we want to go historically and some
39:40of the assumptions that we make in our
39:42calculation so we just we we need to be
39:46aware of the variances of that
39:51input another issue is this risk return
39:54relationship rests on the assumption
39:55that the stock or the asset is priced
39:58correctly um because we're using those
40:01prices for our historical returns
40:04calculations and uh this really rests on
40:08the idea that asset markets are
40:09efficient which you know we know given
40:11recent historical events that and other
40:16things there are reasons to question how
40:19efficient markets are at pricing and
40:21asset at its true or intrinsic value so
40:24the further that uh the asset are priced
40:27away from their intrinsic value well our
40:30historical analysis of returns um you
40:34know it might might throw us off of
40:37it'll throw us off of the true
40:39risks in spite of all these caveats the
40:42capam is is actually widely used by
40:45Financial professionals so this is this
40:47is really it's it's put to use every
40:50day uh among in professional investors
40:54and financial
40:56analysts
40:59summary of this lecture well we started
41:02out by saying we need the expectation of
41:05higher reward for taking on more
41:09risk next we saw that an assets risk
41:13premium is the additional compensation
41:16required above the risk-free rate for
41:19holding the
41:20asset now at the market level the market
41:23risk premium is the additional return
41:26above the risk-free rate to hold the
41:27market
41:30portfolio and for a given asset the capm
41:34tells us how much return will require
41:37for holding that asset relative to the
41:40risk-free rate in the market portfolio
41:42right so it's a really powerful model to
41:46the extent that it is
41:48accurate and uh this was our equation
41:51the generalized equation is simply the
41:53required return equals the risk fore
41:55rate plus beta time the market risk
42:00premium and that wraps up this
42:05lecture

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