Session 4: Equity Risk Premiums

so let's say you have all your money invested in something guaranteed making 2% I come to you with a question how much more than 2% what I need to offer you for you to take your money out of where it's now guaranteed and invest it in stocks the answer to that question is the equity risk premium Now think of asking that question to every investor in the stock market the consent answer you will get across all investors is the equity risk premium you use in valuation that's going to be tough to estimate I know and there are two basic ways that you can estimate it one is to look backwards it's called a historical risk premium essentially you're looking at how much you'd have made in the past the other is to look forward which is a dynamic forward-looking premium that's not as difficult as it sounds and hopefully by the end of the session you will have the tools to be able to estimate a reasonable Equity risk RW almost everybody who does valuation uses an equity risk premium every analyst every company every consulting firm uses it and it's surprises me how little thought often goes into estimating this number so I'd like to spend this session talking about what this number is and how best to estimate it so let's start off by laying the basics the equity risk premium is the premium you would demand you being the investor would demand over and above the risk-free rate for investing in Risky assets equities as a class so think about it if you're making 2% or 3% riskless the question I'm asking is how much more than that would I need to offer you to buy stocks collectively so think about a broad index now as you start thinking about that two things are going to drive the number you're going to come up with one is how risk averse you are as an individual what's going to drive that some of it you're born with some of it is a function of your age but if your risk ofse you're probably going to demand a larger premium second it's also going to depend on what you think about the risk R of equities as a class saying what's going to drive that that's going to be driven by a perception of macroeconomic risk so if you've come off a crisis or you see a lot of uncertainty or volatility in the overall economy you're going to demand a larger premium if you're worried about catastrophic risk the risk that something terrible could happen you're going to demand a larger premium but bluntly the equity risk premium is a number that can and should change over time so as we look at the different approaches keep that in mind any approach that yields the same number year after year after year is probably not that dependable a number now the way most people get Equity risk premiums is to Look Backwards I don't blame them because that's where the data is they look at the past and they ask a very simple question what would I have made investing in stocks over the last 10 20 50 80 years as opposed to investing in something riskless t- BS or t-bonds the difference is a historical risk premium so as an example for over the last 50 years you had thought you'd made 12% investing in stocks each year over those 50 years but you'd have made only 4% investing in treasury bonds over that same period 12 - 4 would have yielded an 8% historical risk premium that should be pretty simple to do right especially in a market like the us we have a long history take a look at that table at the bottom of this page you'll see three slices of History I've taken one goes back to 1928 it's 85 years of History one goes back 50 years one goes back 10 years I get very different estimates of the risk premium depending on how far back in time I go I get a very different premium with 85 years as opposed to 10 what I use is my risk-free investment I use t-s at a short-term government as opposed to T bonds which are long-term and whether I compute arithmetic averages or geometric averages you're saying what the heck is that sounds like inside Statistics but here's the difference arithmetic averages I add up 85 numbers and divide by 85 it's a simple average geometric averages I take take into account the compounding that happens over time so depending on the decisions you make on estimation your Equity risk premium could be 7 7 and 1. 2% or it could be 1 1 and a 12% all these numbers can't be right at the same time but here are the two things that I would like you to keep in mind one is whenever you estimate a risk premium looking at the past it's a statistical estimate it's an average over time that average comes with a standard error that again is something we tend to to forget after our statistics classes but those standard errors carry a message take that 4. 2% that you saw on the previous page as my risk premium over an 85-year time period that is the geometric average premium for stocks over t- bonds over 85 years that sounds pretty precise right 4.

2% but before you get too excited about that number take a look at that 2. 33% you see in Brackets right below that period That's My standard error so think about it when I tell you the historical risk premium is 4. 2% what I'm not telling you is the standard error in that number is 2.

33% which means my true premium could be less than zero be higher than 9% and that's with 85 years of history with 10 years of History I might as well not look at that number because the standard error is so large so that's the first problem with historical premiums is the estimates you get are noisy which is just a fancy way of saying they're error prone the second problem and especially when you use the US data you face this problem is you have a survivorship bias what am I talking about the most successful Equity Market of the 20th century was a US market using that market to estimate a forward-looking premium assumes that I will know what the most successful Equity Market is for the next century and I don't so a better measure of historical premium might average out the premiums across multiple markets and there are databases that do that having said all of that though a his historical premium is a flawed way of thinking about Equity risk it's backward looking it assumes that everything reverts back to Historic Norms that might have been okay in the old days 2005 1995 1985 but I think the crisis of 2008 should have shaken your faith in things reverting back to normal what I'd really like is an equity risk premium looking forward and I think there's a way to do it to get a sense of what I'm going to do next let me give you a sense of what the calculations involve you know how to compute the yield to maturity on a bond you take the price of the bond you take the coupons as the cash flows you include the face value and the yield to maturity is that discount rate that makes the present value of your cash flows equal to the price of the bond we do this with fixed income all the time but let's assume that we can do this with equities instead of buying a bond let's assume you bought the S&P 500 at the start of 2013 you know what that have cost you 1,426 one9 so instead of buying a bond you bought the entire index 500 largest market cap stocks right instead of coupons what do you hope and pray you get hope and pray you'll get some cash flows right those cash flows will take the form of either dividends and with us companies some BuyBacks I can't tell you what they will be in the future but I can tell you what they would have been last year that's easy enough to do I just count up the dividends and BuyBacks across all us companies so I know what you paid for stocks I know what the cash flows were last year I bring one final piece into the puzzle analyst in the US often estimate growth in earnings for the S&P 500 I collect those growth numbers and based on those growth numbers I project out an expected growth in cash flows for the next 5 years of 5. 27% I'm almost home I take the cash flow from last year I grow it at that 5. 27% at some point in time I assume that that growth rate will revert back to the growth rate of the economy and I use the risk- free rate as my proxy for that and we'll come back and talk about why and I'm pretty much set on Computing an equivalent to the to the yield to maturity I have the price for stocks what you paid 14 2619 I have the expected cash flows I solve for that discount rate that'll make the present value of my cash flows equal to the level of the index today it's a little messy but I can get there and when I get there I have an expected return on stocks at the start of 2013 that number was 7.

54% you say how how are you going to use that remember the risk free rate the t-bond rate at that time was 1. 76% the difference of 5. 78% is my estimate of a forward-looking equity risk premium at the start of 2013 you know what's neat about this you can recompute this number the next day and you get a different number it's forward-looking and it's Dynamic to to give you a sense of how this number shifted over time take a look at this graph so if you look at this graph then you have the implied premiums over time now you might wonder why do we care about implied premiums implied premiums carry a message that we ignore at our own Peril let's take an example let's suppose to start of 2013 and you work at an investment bank or an equity research house everybody in the bank uses 4.

2% that historical risk premium to Value companies but the implied premium is 5. 8% you know what's going to happen right use a 4. 2% premium everything is going to look cheap to you why because you used too low of Premium not because this company is a great investment but because you think the market is cheap so even if you decide not to use implied premiums I think it behooves you to at least know what it is at any point in time so all of this talk we've had so far is about estimating Equity risk to the US where you have a luxury of data you have historical data going back 100 150 years you have all the data you need for implied premiums you're saying what do I do though if I have an Indian company an Indonesian company a Chinese company a Brazilian company in other words an Emerging Market where you don't have a lot of data let me suggest a couple of things you can do to estimate risk freams in these markets one is to build off a measure we used in a previous session to get to a risk free rate remember how we did that we started with the government bond rate we came up with a default spread for the country we netted that default spread from the government bond rate to come up with a risk- free rate now I'm going to use that default spread again to get to an equity risk premium and here's what I'm going to do I'm going to start with that default spread the case of Brazil it's 1.

75% then I'm going to look up two more numbers one is the standard deviation in the Brazilian Equity index in this case I used the basa it came up at 21% the other is the standard deviation in that Brazilian dollar denominated bond that I used to look up the default spread and that number was 14% he's saying where are you going with us if you look at the 21% the 14% it looks like the Brazilian Equity index is about 1 and half times more volatile than a Brazilian Bond that's 21 divided by 14 if I scale up the default spread of 1. 75% for that additional risk I come up with about 2. 63% I add that 2.

63% to my base premium for the US which let's assume is 5. 8% based on my implied premium I have an equity risk premium for Brazil so let me recap start with the mature Market premium look up the default spread for the country you're interested in scale that spread up if you can if you can't just use the default spread and just add it on to the mature Market premium you have an equity risk premium for a country now I could also use an implied premium it's a little trickier when I use an implied premium because I have to get those same inputs for Brazil that I got for the US which is the cash flows from the most recent year which is not a problem the index level from the most recent time period which is not a problem and an expected growth rate which might be a bit of a problem but if I can get an implied premium for a market I can bypass this process and tell you what the equity risk Bram going forward is for a country so in this graph for instance I've tried to map out the implied Equity risk Fram for Brazil versus the implied risk Fram for the US and note something interesting note how much the additional Premium charging for Brazil has dropped over the last decade Brazil today is a lot less risky at least in the eyes of investors than it used to be so use either the rating based default spread based approach or an implied premium to come up with risk premium by country at the start of every year I actually develop a table of equity risk premiums by country there's no magic to this table I start with the base Prem so this is the table from the start of 2013 I use the 5. 78% I estimated as my implied premum for the us as my base I rounded up to 5.