We would like to preface this article by making it clear that we're not making any market crash predictions. Instead, we will be looking into the mechanics of the market to come up with a framework for understanding how it functions. These are simply some ideas that we'd like to share. We're interested in reading any feedback on whether you agree or not. If you disagree, we'd appreciate your thoughts to be constructive so that we can collectively try to arrive at a better understanding. A lot of the time, the market appears to wild, irrational and random. However, there's a potential method to the madness. In the grand scheme of things, the market is mechanical and influenced by a few key factors. Namely, the bond market, discount rates, and growth expectations. No surprises there. But how can we organize these factors to arrive at an understanding of what is driving the markets? Is the Market in a Bubble?We often see investors reference the historical P/E ratios to conclude that the market is overvalued. Although this is a good start, it has a flaw. When will the P/E multiple revert to the mean? Looking at history and recognizing that prices are higher than normal won't necessarily stop prices from continuing to go up. This could cause investors to miss out on solid gains, which reminds us of the quote from Peter Lynch:  "Far more money has been lost by investors preparing for corrections or trying to anticipate corrections than has been lost in the corrections themselves." Of course, it's probably better to be out early than late, but we want to improve our chances of getting out closer to the top. But there remains a question  why and how do stocks form bubbles? Well, the answer might be that it's not a bubble until it gets close to the top. Bear with us. What we mean is that it's likely not mainly due to irrational investors. Although they play their part, the underlying fundamentals brought the market to a certain height and then quickly changed for the worse. Bond MarketWe'll start with the bond market. The bond market, in our opinion, is probably the best gauge for the stock market. Government bonds form the basis of valuation as the 10year yield is often used as the riskfree rate. Changes in the riskfree rates impact the valuation of equities. Therefore, what happens in the bond market is a precursor to what may happen in the stock market. The main driving forces behind the bond market are inflation expectations and the Federal Reserve. Emphasis on the word expectations because the market is forwardlooking. If the market expects inflation to drop in the next 612 months, bond yields will drop as well. The opposite is true if inflation is expected to rise. The Federal Reserve impacts the bond market by buying or selling. When it buys bonds, it pushes yields down and vice versa when it sells. This is how central banks print money. Essentially, they're paying investors who are selling bonds with money that didn't previously exist. This money doesn't directly make its way into the economy because it goes to investors who liquidated their positions in an investment account. Because the investor just lost a source of income in the form of interest payments from the bond, it's very likely that this money will simply be reinvested. Since yields are low, other assets such as stocks or real estate become more attractive and money begins flowing into those asset classes. When the Federal Reserve sells bonds, it's removing money from the market and pushing yields higher. As a result, bonds start becoming more attractive. Discount RatesNow that we've discussed the bond market, it's time to move on to the discount rates. The discount rate is the theoretical minimum required rate of return an investor demands from an investment. The most commonly used method to calculate the discount rate is the capital asset pricing model (CAPM for short). The formula is as follows: CAPM = Riskfree rate + Beta (Equity Risk Premium) We understand that CAPM is mainly used for individual stocks. However, when breaking down the theory behind the CAPM, we can see why it makes sense to use it for an index. We will start with the equity risk premium which we will refer to as "ERP." The ERP is written as the expected return of the market minus the riskfree rate. The "market" that investors use for the calculation is almost always the S&P 500. The theory is that to compensate for the additional risk of equities as a whole, investors require a certain return over the riskfree rate to justify investing in this asset class. The equity risk premium that's most commonly used is the historical one which is calculated as historical S&P 500 returns minus the historical riskfree rates. Currently, that's 4.7% as per data from Finbox. Now, the part that applies to individual stocks is the beta portion of the formula. The theory is that to compensate for the additional risk of investing in an individual stock versus a diversified portfolio of 500 stocks, the equity risk premium needs to be adjusted by the volatility of the individual stock. This represents the premium over the riskfree rate that investors require to justify investing in the individual stock. Finally, the current riskfree rate is added to the adjusted ERP to get the end result (remember, ERP is the amount required above the riskfree rate). Since the required return for the S&P 500 as a whole already is part of the ERP portion, and we're not adjusting for the risk of an individual stock, the CAPM formula in this scenario can be simplified as follows: CAPM = Riskfree rate + Equity risk premium As you can see from the formula, all else being equal, the higher the riskfree rate, the higher the discount rate which equates to a lower valuation of stocks. This is consistent with the notion that higher yields make stocks less attractive. Therefore, we believe using CAPM to determine the discount rate of the index is a reasonable approach because the required return of the index already is part of the calculation. In addition, an S&P 500 index ETF is an asset that owns 500 profitable companies. To purchase this asset, you need to pay a multiple over the total earnings. Therefore, trying to determine a fair value is a logical thing to do. Expected Growth RatesIn addition, it's important to remember that the market is forwardlooking. Thus, growth expectations are an important piece of the puzzle. Market panics can arise from a very pessimistic view of future earnings. The pandemic crash was caused by the initial expectation that lockdowns would severely impact the future earnings of most businesses. Put all these pieces together and you can get a reasonable understanding of what is driving the market. Many found it strange in 2020 when the economy was crumbling while the S&P 500 was heading straight up towards a Vshape recovery. But, when we look at the factors we mentioned above, everything lined up perfectly for that rally. Yields went from nearly 2% at the start of the year to as low as 0.33%. This caused discount rates to drop considerably which boosted the valuations of stocks that saw minimal impact or benefited from COVID19. In addition, the market expected the economy to eventually recover while at the same time expecting COVID19 beneficiaries such as bigtech to see a surge in growth. Then as 2021 rolled around, inflation expectations began to rise while growth expectations for stayathome stocks began to fall. As a result, the riskfree rate increased along with discount rates. During this time, tech stocks took a hit because they had higher valuations which could no longer be justified by the discount rates and growth expectations. The S&P 500 Index pulled back a little bit as a result. However, it quickly rebounded because the recovery stocks were now expected to see strong enough growth from reopening that their valuations still looked attractive at higher discount rates. Since then, tech and recovery stocks have been taking turns rallying and falling depending on the changing conditions each month causing the SPY to essentially go up with only minor pullbacks. Putting It All TogetherBased on the factors mentioned above, we want to be able to answer 3 questions:
The fastest way to value companies is by using multiples. Thus, we need to figure out what the right multiple should be. We will begin by setting earnings to 1 to represent 100% of all the profits earned by companies in the S&P 500. Next, we will need a discount rate. As already discussed, the CAPM formula can be simplified as follows: Riskfree rate + Equity risk premium At the time of this writing, the 10year yield is 1.49% and the equity risk premium is 4.7% as per Finbox, which equals a discount rate of 6.19%. If we didn't want to factor in growth, we could simply say that the fair value of the S&P 500 is 16.15 times earnings: 1 ÷ 0.0619 = 16.15 However, that's incomplete because growth expectations are important. Since the market tends to look 612 months ahead, we will incorporate growth for the next 12 months. For growth estimates, we will use analyst estimates which can be found here. The latest reporting period for S&P 500 earnings is June 30, 2021. As of that date, the trailing twelve months EPS for the S&P 500 is $158.74. Looking forward to June 30, 2022, EPS is expected to come in at $187.11 on a TTM basis. This represents an expected 17.87% growth rate. However, earnings are likely to continue growing in the long run. Therefore, we will need a perpetual growth rate which we set to 2.06%. We arrived at this number by using the 30year treasury yield as a proxy for longterm growth expectations. This number fluctuates constantly, you can check the current 30year yield here. Since 30year bonds are the longest duration bonds, it makes sense to use their yield as the perpetual growth rate. Fair Value = (1 + NTM growth) ÷ (discount rate  perpetual growth rate) 28.54 = 1.1787 ÷ (0.019  0.0206) At the time of writing, the S&P 500 is trading at about 27.3x earnings (calculated as follows: 4333/158.74 = 27.3) which means it's still below the fair value of 28.54x that we just calculated. A multiple of 28.54x implies a price of about $4530 for the S&P 500. This isn't too far off certain price targets that are calling for S&P 500 to hit $5,000. The beauty of this approach is that you can automate the inputs on Excel or Google sheets and see the fair value change in realtime and thus be ready for sudden changes in market conditions. LimitationsThere are some limitations to this approach. To begin with, there's some degree of subjectivity when it comes to the perpetual growth rate. Different investors might have slightly different expectations for perpetual growth which could make a material impact on the valuation. However, to add a bit more objectivity to the calculation, we think the most reasonable approach is to use the 30year treasury yield as it can be used as a proxy for longterm expectations. In addition, the market's expectation of earnings growth for the next 12 months can change very rapidly. Thus, investors have to stay on top of these expectations to avoid being blindsided. You could use analyst expectations like we did in our calculation. However, that assumes normal market conditions. Black swan events are therefore not factored into these estimates. Final ThoughtsThis is not a perfect solution. However, we believe it provides a reasonable framework for understanding the mechanics of the market quickly. It also provides better guidelines for when to buy and sell at a macro level so that you can capture more gains and reduce the risk of being blindsided by changing market conditions.
We understand that some people are not fans of the CAPM model. However, as investors, we must understand that what matters most are the methods that most other market participants use. CAPM is still the most popular method for determining discount rates and changes in the riskfree rate will continue to move markets. Therefore, we believe it's better to listen to what the market is saying through the use of discount rates rather than trying to tell it what to do 
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