In the previous piece, I offered a definition of the investment concept of “intrinsic value.” Intrinsic value is the value that the owner of a security realizes from holding the security, rather than selling it.

To determine the intrinsic value of a given security, we can apply a simple test. We posit that the security that cannot ever be sold, but must be held until maturity. We then ask ourselves: what is the maximum price that we would be willing to pay, or alternatively, the maximum amount of cash that we would be willing to exchange, to own the security? That amount of cash must equal the intrinsic value of the security, the value that accrues to us simply from owning it, otherwise the exchange would not make rational sense.

In this piece, I’m going to explore the set of fundamental considerations that would impact a rational agent’s assessment of the intrinsic value of different types of securities. The analysis will seek to clarify “the way things ought to be” in financial markets–the way they would be if everyone invested rationally, based solely on the intrinsic value contained in the investment opportunities presented.

To be clear, “the way things ought to be” in financial markets is not the way things actually are, particularly with respect to long-dated assets, assets whose maturities are too far out in the future to “wait for.” Market participants that trade and invest in long-dated assets do so based not on estimations of “intrinsic value”, but rather on estimations of how the prices of those assets will evolve over the short-term to medium-term, a few months to several years, which is the limit of human look-forward capacity, and the time horizon on which investor performance is measured. Investors are not able, personally or professionally, to seriously consider longer time horizons, on the order of decades or even centuries, even though that is often how long it takes for the “intrinsic value” of long-dated assets to play out.

Investors worry about the “fundamentals” of long-dated assets not for their own sake, but because the fundamentals influence the prices, through non-fundamental perceptual and behavioral channels. The fundamentals serve as subjective inputs into the minds of investors, factoring into the rule-based calculations that drive actions and outcomes in the market: “X is happening, it probably means Y. From a portfolio standpoint, the right move is probably for us to do Z.”

Cash, Bonds, Stocks, Other

Investors are confronted with a range of different types of assets in which to hold their wealth. We can simplify this range into four categories: Cash, Bonds, Stocks, and Other. To determine the “intrinsic value” of assets in each category, we need to express them in terms of cash, which is the basis for measurement.

Cash is just cash, money, whatever must be accepted by law to repay debts, public and private. The prices of all assets are expressed in terms of it, therefore the intrinsic value of one unit of it is one. Bonds are a finite collection of more-or-less guaranteed cash payments, usually consisting of small cash payments for a time (coupons), followed by a large cash payment at the end (return of principal). Equities are an infinite collection of non-guaranteed cash payments (dividends, or rental payments on the use of capital, land, housing, and so on). The “other” category consists of unproductive assets, assets that do not generate a cash flow–think, gold bars. These assets have very little intrinsic value, and are almost always purchased with the intent of eventually offloading the investment onto someone else.

The dividends that shares of equity pay out to their owners tend to grow at a rate that exceeds the rate of inflation. The reason is twofold:

First, the dividends are backed by corporate earnings, and are paid out as a percentage thereof. On a unit basis, corporate earnings equal price minus cost. Inflation–a change in the price index–acts to increase both of these entries equally, therefore it acts to increase their difference—earnings—equally as well.

Second, not all of the earnings are paid out as dividends. Some of the earnings are used up in the purchase of growth. The amount of growth purchased adds additional earnings, and therefore additional dividends, to the numbers of the future.

Now, to be clear, funding costs–for example, dilution–can cause per-share earnings to not keep up with inflation, particularly when the corporate sector is inefficient in its use of the proceeds. In the present context, we will assume that corporations fund their growth internally, without increasing share count (an assumption that has proven valid in recent experience), rendering the issue of dilution moot.

Leaving the “other” category aside, we are left with two types of assets whose intrinsic value we want to measure: bonds and shares of equity. So we return to the critical question: how much of each type of asset would we be willing to exchange for cash, if we could not ever go back on the exchange?

A bond is just a future stream of small cash payments (coupons), followed by a final payment (repayment of principal). How much cash, held in hand right now, would we be willing to trade for that future stream? The answer, for us, is the intrinsic value of the bond.

A share of equity is a future stream of small, growing, inflation-linked cash payments, without a maturity date. How much cash, held in hand right now, would we be willing to trade for that future stream? The answer, for us, is the intrinsic value of the share of equity.

The Time Value of Money

Money now obviously is not the same as money later. Money now is better, for a myriad of reasons, not the least of which is that it can be used now, at the option of its owner. Money later, in contrast, cannot be used until it is received.

The difference between money now and money later is the “time value of money.” Looking at the current state of bond prices in the developed world, we might think that money has no time value to current investors. After all, long-term bonds in the developed world trade at prices with implied yields approaching zero. An investor who lends his money to a government in the developed world for five, ten, twenty, even thirty years, gets essentially nothing in return–nothing except the original money that was lent out, for a net nothing.

But to conclude that money has no time value to current investors would be a huge mistake. The reason that current investors are willing to lend their money to governments at zero rates of interest for prolonged periods of time is that they know they can easily get out of the loans by selling the associated securities back into the market. For all intents and purposes, in a liquid market, where investors are confident that they will be able to sell their investments at or near cost, the “time value of money” loses relevance. The assets become the functional equivalents of “money now”, given that they can be converted into “money now” at the push of a button. In purchasing the asset, the investors don’t have to “part” with their money, therefore they don’t have to put a price on the cost, to them, of “parting” with it. If they did, the price dynamics observed in developed world bond markets would be very different from what they are.

Take any institutional fund that is currently eager to lend its money to the Swiss or Japanese governments for decades at near-zero interest rates, and tell that fund that it will have to hold the associated debt security until maturity–that it will not, under any circumstances whatsoever, be allowed to get the money back by selling the security to other investors (or engaging in any “tricks” that might simulate a sale, such as posting the security as collateral for a loan, or selling short a similar security). You would quickly see the time value of money come back into play, in a dramatic way. To be sure, it is not zero. Not even close.

When word gets out that a financial institution is in trouble and is facing a liquidity crisis, its customers rush to redeem their money. The main fear that drives their behavior isn’t the prospect that the money will be lost forever–the investors know they will almost surely get it back, after everything has been cleaned up, years later. Their most pressing worry is actually the prospect that the money will get stuck inside of a black hole in the interim–a confused, entangled “what belongs where?” scenario, a court battle involving complicated and drawn-out litigation–and that the customers therefore won’t be able to access the money for months, years, maybe decades. Ouch. Again, we see the importance of the “time of value of money”–when it is actually at stake. In a stable, liquid market with a confident bid, it is not at stake, and so it doesn’t factor in. But things can easily and quickly happen to put it at stake, which is why long-term assets–assets with maturities on the orders of many years, decades or centuries, that cannot realistically be “waited out”–are prone to violent bouts of volatility, when confidence in the presence of future bids near the current price is lost.

The Exercise

Cash held in the banking system carries essentially all of the benefits of cash held in hand, with a number of additional perks and conveniences. For this reason, individuals usually choose to hold their cash in banks, in the form of deposits. The banks normally pay interest on the deposits, which they fund through the income they generate on their loans. Without getting into the details, central banks in modern financial systems have the ability to adjust the rate of interest that banks, in the presence of market forces, have to pay on their deposits. Expectations with respect to the future path of this rate of interest have a substantial effect on the “intrinsic value” of all other assets, because all other assets must compete with it.

To illustrate, let’s do the exercise. You have $100,000 in wealth, and three modalities in which to store it:

(1) Cash: You can hold the wealth as a cash deposit in an insured bank, and earn interest on it. While in the bank, you will be able to spend it on consumption. Depending on the nature of your deposit, you may have to wait a few weeks to spend it, maybe a month or two, but you can afford to wait that long. To keep things fair, let’s suppose that if you choose this option, you can only spend the money on consumption–you cannot go and invest it in the other options later. You will have to make the “investment” decision now, and you will have to stick with it for good, at least as far as that money, the $100,000, is concerned.

The interest rate that you will be paid will be determined by the central bank, chosen so as to bring the rate of inflation–and any other macroeconomic target that the central bank might have–onto target. In periods where there are strong inflationary pressures, the rate will be increased, so as to incentivize you and others to hold your cash rather than spend or invest, and to disincentivize others from borrowing it to spend or invest. The same is true in reverse: in periods where inflationary pressures are weak or negative, the rate will be reduced, so as to disincentivize you and others from holding your cash, get you to spend or invest it instead, and to incentivize others to borrow it to spend and invest.

(2) Bond: You can buy (miniature) 10 year treasury bonds. Each bond pays guaranteed fixed interest payments of $60 per year, followed by a large principal repayment, $1,000, in 10 years. Importantly, you cannot sell one of these miniature bonds after you have bought it. You must hold it to maturity. The money that is figuratively “contained” inside it will be locked up, unable to be used by you in any way, until then.

(3) Equity: You can buy diversified shares of equity, say, the 500 companies of the S&P 500. The share pays $40 per year in dividends, the dividends grow anywhere from 1% to 4% per year, plus inflation, with a sharp recessionary drop every several years that is eventually fully recovered. Crucially, the shares have no maturity. You will never get the original principal back–what you will get back is an ever-growing stream of dividends, which over the very long-haul, will exceed what you put in by many orders of magnitude.

We have not yet stated the per-share price of the bond and the equity. The goal here is for you to seriously think about the options, as if they were presented to you right now, and identify the maximum price that you would be willing to pay for each share, the maximum amount of cash that you would be willing to permanently exchange for them–which, for you, is the “intrinsic value.”

As a rational agent, what do you need to know in order to determine the “intrinsic value” of each type of security? For starters, you need to know, or estimate, the concrete specifics of the payout stream. How much is the bond going to pay? How much is the cash going to pay? How much is the equity going to pay?

For the bond, you already know the entirety of the future stream–$60 per year, plus $1,000 in ten years. The stream carries no uncertainty in its payouts. But knowing that alone is not enough. You also need to know the nominal interest rate that cash in the bank will pay you over the next ten years. It will not make rational sense for you to pay a price for the bond that implies a return that is any lower than that, any lower than what you can get in cash, because cash also affords you the precious ability to have the money and use it, which the bond does not afford you. Therefore the bond needs to be priced to pay you more.

Now, we know that the central bank is going to set the cash interest rate so as to control inflation. So the true variable that matters here is the future neutral nominal interest rate, the nominal rate of interest that the central bank will have to set going forward, given the structural dynamics of the economy, in order to keep inflation and any other target that it might have–employment, foreign exchange control, financial stability–on target.

In truth, of course, you’re going to demand even more than the expected neutral nominal rate, you’re going to demand a premium to compensate you for the time value of money, the cost of losing the ability to use your money. How much you demand will be determined by the amount of value that money in hand has for you in comparison with money promised in the future.

How different, for you, is “money now” from “money later”? The answer will obviously depend on the myriad of complex psychological and economic factors that define your unique personal situation. How much do you value the comfort and security of having access to your money, the ability to use it if you should want to use it, or need to use it? How much more valuable is that kind of money to you, in comparison with money that will be locked away for a long period of time, inaccessible to you? How many things are there in the economy for you to buy right now that might tangibly increase your happiness, or the happiness of those you care about? How old are you, and to what extent is the money needed to fund your desired consumption expenses? If the money is needed, will the coupon or dividend payments that will accrue on it if it is permanently locked away in a bond or an equity be large enough to fund those expenses? If so, then you may be fine with seeing it locked away, given that you can get by on the infinite payouts that will accrue. What are your expectations with respect to inflation? Inflation eats away at the future purchasing power of money. High inflation therefore widens the difference between “money now” and “money later”, given that it makes “money later” into “less money.” All of these variables, and a number of others, will factor into your estimation of the “time value” that money has for you.

To summarize the bond case, then, we’ve identified two variables that matter to the intrinsic value of a long-term treasury bond: (1) the expected neutral nominal interest rate on cash over the life of the bond, which sets the minimum floor for what you can rationally accept from the bond, given that you have the alternative of holding cash, and (2) the time value of money, which you ultimately have to specify for yourself, given the unique psychological and financial details that characterize your individual situation.

For the equity case, the evaluation is more complex. We need to estimate the future growth of the dividends, and by extension, the future growth of the earnings out of which they will be paid (and which will pay for their future growth). In the scenario, we set a range of 1% to 4% after inflation, but that’s a huge range–any information that pushes the number in either direction is going to be very important.

We can separate the growth of dividends into two components: real per-share growth, and inflation. The first component is determined primarily by the health and dynamism of the underlying economy, and by the efficiency and capital allocation skill of the aggregate corporate sector. The second component is driven by culture, demographics, supply constraints and policy.

The two factors that were relevant to the intrinsic value of the bond–the expected neutral nominal interest rate and the time value of money–are just as important to the intrinsic value of the equity. As with the return produced by holding the bond, the return produced by holding the equity competes directly with the alternative of holding cash in the bank and collecting the future neutral nominal interest rate. Similarly, holding the equity instead of the cash entails loss of a large amount of money that would otherwise be accessible.

What we end up with, then, are four variables that determine the “intrinsic value” of the equity: (1) the expected neutral nominal interest rate, (2) the time value of money, (3) the expected future rate of real per-share growth, and (4) the expected future rate of inflation.

Now, here comes a critical move. We can combine (4) and (1) into a single variable, the expected neutral real interest rate. Going forward, what real interest rate, after inflation, will the central bank have to set in order to maintain inflation, and any other targeted macroeconomic variable, on target? That rate is critical, because it expresses the difference between (a) inflation, a crucial component of the nominal growth that the equity payouts will exhibit, and (b) the nominal interest rate that the cash holdings will earn.

The Fed Model

The Fed Model is a popular a method of measuring equity valuations. The model assesses valuation by comparing the earnings yield on equities to the long-term government bond yield. When equity earnings yields are substantially higher than the long-term government bond yield, equities are said to be cheap. When equity earnings yields are not appreciably higher than the long-term government bond yield, equities are said to be expensive, or at least neutrally priced.

In practice, the Fed Model has caused a number of analysts to push back on the growing consensus that the US stock market is expensive, while Emerging Market stock markets are cheap. These analysts acknowledge that earnings yields in the US are lower than in the Emerging Markets (or alternatively, that P/E ratios in the US are higher than in the Emerging Markets), but they point out that we cannot talk about yields and P/E ratios in a vacuum. We have to compare them to the available alternatives, the attractiveness of which are captured by prevailing interest rates.

But this way of thinking is partially wrong. It ignores the fact that interest rates are typically set at low or high levels in response to low or high levels of another variable that matters greatly to equity returns–inflation. Why has the US central bank set the interest rate at a low level? Because the US does not have enough inflation. Why has the Brazilian central bank set the interest rate at a high level? Because Brazil has too much inflation. The low inflation in the US contributes to an environment of low nominal earnings and dividend growth, and therefore low nominal total returns, all else equal (and note that all else is not equal, in this case). The high inflation in Brazil (or Argentina or Zimbabwe) contributes to an environment of high nominal earnings and dividend growth, and therefore high nominal returns, all else equal. The Fed Model fails to capture and factor in the impact of this crucial difference.

If we’re going to connect P/E ratios to interest rates, as the Fed Model tries to do, the interest rates that we should use are real interest rates, interest rates that take out expected future inflation, which is a significant component of nominal equity returns. When we do this, we see that a number of emerging markets with high interest rates and high P/E ratios, such as India, deserve to have high P/E ratios, because their real interest rates are very low, if not outright negative (making cash and bonds that much less attractive in comparison with inflation-linked equities). Similarly, a number of countries with low interest rates, such as Japan under pre-Abenomics deflation, deserve to have low P/E ratios, because their real interest rates are high (making cash and bonds that much more attractive relative to inflation-linked equities).

Foreign Equity Investing

This dynamic extends quite elegantly to the realm of foreign equity investing. To use the example of Brazil, Brazilian equities currently sell at very low P/E multiples–at last check, around 8-9 times, with correspondingly high dividend yields and substantial room for P/E multiple expansion over the long-term. For this reason, many US investors, frustrated with the lack of attractive options at home, have explored the country as a potential investment opportunity.

Suppose that you are a US investor that wants to capture the return potential of the Brazilian equity market. But you want to capture that return in dollar terms–the terms of your own currency. If the Brazilian market goes up 200% over the next 10 years, you want the value of your Brazilian investment, in your own currency, the Dollar, to achieve that same return. The only way that you can make this happen is by hedging the currency. You would go simultaneously long the Brazilian stock market, and short the Brazilian currency, the Real. Then, your return in dollars would exactly mimic the local currency return of the Brazilian stock market.

But there’s a problem. The cost of shorting the Brazilian currency is the Brazilian interest rate; you will have to pay that interest rate to whomever you borrow the currency from in your short. Right now, the rate is quite high, north of 10%. That 10% will represent a significant drag on your returns. For this very reason, it’s impossible for you to create a dollar-denominated investment that will exactly track with the Brazilian stock market. The best you can hope to do is create an investment that tracks with the Brazilian stock market minus 10% per year.

Not all is lost, of course. Your investment might still produce an attractive return, even in the presence of the high carry. The interest rate in Brazil is high, 10%, but that’s because inflation in Brazil is very high–well north of 6%. The 6% inflation is going to add to the nominal growth in Brazilian earnings and dividends. When combined with the high dividend yield, and the significant multiple expansion that is likely to occur as sentiment improves, the return that the investment might be able to make up for the 10% carrying cost.

What we need to do in a valuation analysis is combine these two numbers–the inflation and the interest rate–since they offset each other in terms of their effects on the return. The inflation adds to the return, and the interest rate–which is the carrying cost–subtracts from it. The combination of the two, of course, just is the real interest rate, which, you will recall, is what we found to also be a critically important variable in the determination of the intrinsic value of domestic equities.

The real interest rate in Brazil is 10% minus 6% which equals 4%–on the high side globally. For this reason, Brazil probably should have a lower P/E multiple than the developed world, where zero or negative real interest rates have become the policy norm.