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Trader Gregory Rowe works on the floor of the New York Stock Exchange, Friday, May 26.Richard Drew/The Associated Press

With U.S. stocks reaching new records almost daily, there's an endless discussion about whether equities are cheap or expensive. Bloomberg Gadfly columnist Nir Kaissar and Bloomberg View columnist Barry Ritholtz met online to debate the valuation question.

Kaissar: Everyone knows that U.S. stocks look expensive relative to the rest of the world. The Standard & Poor's 500 Index has outpaced both the MSCI EAFE Index -- a collection of developed market stocks outside the U.S. -- and the MSCI Emerging Markets Index by 6 percentage points annually since March 2009, when the market hit bottom, through May, including dividends.

Valuation aficionados love to argue about which yardstick is best -- price-to-earnings ratio, price-to-book or price-to-cash flow. But this time there's no argument. All three measures point to higher stock prices in the U.S.

Rather, the arguments are over more difficult questions. Why are overseas stocks so much cheaper than U.S. stocks? Are overseas stocks riskier, or are they mispriced? And what if anything should investors do about current valuations?

Ritholtz: I look at equity valuations from a different perspective. There are three things investors should take note of: "Fair value" is simply a point that stocks careen past on their way to being either cheap or expensive. Valuation cycles are driven by psychology; during bull markets, investors become willing to pay more and more for a dollar of earnings; bear markets see the opposite. Eventually, mean reversion reasserts itself and the regional performance gap between the U.S. and Europe will reverse. Of course, getting the timing of this right is very, very tricky. One last thing to keep in mind: the U.S. has been trading at a premium over the MSCI EAFE and MSCI EM indexes for a few years -- more often than not, the markets see good reasons for those higher valuations.

Kaissar: I agree that valuations are cyclical. But whether those cycles are driven by behaviour -- or in Barry's parlance, psychology -- or risk is a critical distinction.

The view favoured by buy-and-hold investors is that low valuations reflect higher risk, so there's no free lunch (or alpha, in geek speak) available from buying cheap assets. On the other hand, if valuations reflect only the mood of investors, the implication is that value and risk can decouple and that investors may be able to exploit that decoupling.

I tend to favour the behavioural explanation in this context, and I think the current environment is a good example. The price-to-book ratio of the S&P 500 is now twice as high as that of EAFE and EM. Can we credibly say that the U.S. is half as risky as those other regions given the U.S.'s multiyear struggle to kick-start its economy and its recent political turmoil? I don't think so.

Now the harder question is whether investors can exploit these valuation gaps.

Ritholtz: Let's make sure we are all using the same definition of risk: I define risk as the probability that actual returns on an investment will be lower than the expected returns. Not volatility, drawdowns or losses, but less-than-expected returns. What expected returns should long-term equity investors reasonably anticipate? About 10 per cent with dividends reinvested, which is what an S&P 500 total return fund generated from 1990 to present -- 10.04 per cent to be exact. Where valuation comes into this is periods when stocks are expensive; your expected returns should go down proportionately. Similarly, when stocks are cheap, your expected returns are likely to be higher. However, that is just the average -- there are years where expensive stocks saw double-digit appreciation (the 1990s) and years where cheap stocks did very poorly (the 1970s). It is a complex and often nonlinear relationship. Hence, the perception of risk is certainly a psychological element, one that can manifest itself in investor behavior of buying or selling.

Kaissar: I'm not quite ready to dismiss volatility and drawdowns as barometers of risk. Investors are more likely to abandon high-volatility or high-drawdown assets at the wrong time than ones with lower volatility and drawdown. So it's worth considering how an investment is likely to behave.

Volatility and drawdowns have another virtue, too: They're measurable. For example, the earnings yield for the S&P 500 is 4 per cent and the yield for EAFE is 6.3 per cent (using 10-year trailing average positive earnings). Let's assume for the sake of argument that the earnings yield is a good proxy for expected return.

One can test whether higher earnings yields have been associated with higher volatility or larger drawdowns. Granted, historical data is never dispositive, but it can be instructive. If you conclude that EAFE's higher earnings yield means a bumpier ride, then there's no reason to prefer EAFE over the S&P 500 on a risk-adjusted basis. If you don't, then EAFE may be the better bet.

But however one defines it, risk in this context is simply a vehicle for answering the broader question: Namely, should investors prefer EAFE because it has a higher expected return than the S&P 500?

Ritholtz: It's an old joke to say that not everything that matters can be measured, and not everything that can be measured matters. Back to EAFE versus EM versus the U.S.: The thing is, you don't have to pick one over the other. You can (and should) have exposure to all of these various asset classes. But first, let's acknowledge the elephant in the room, namely valuations: Based on the relative expense of U.S. stocks when compared with other developed and emerging markets, the U.S. markets are quite pricey. Value investors are advocating a shift away from the U.S. and into these other regions. But here's the thing: The pundits were making these exact same suggestions three, four and five years ago. Had you followed their advice then, you bought into "submerging" markets and a European mess, while the U.S. still had lots of upside to go. The evidence suggests to me that rather than timing which part of the world is going to do better or worse, it's better to own it all. The alternative is playing a guessing game that history suggests few, if any, are especially good at.

Kaissar: You raise two points that are worth unpacking separately.

The first -- and easier of the two -- is that there's too much home bias in U.S. investors' portfolios. U.S. investors commonly allocate 70 per cent to 80 per cent of their stocks to the U.S. By contrast, U.S. stocks represent roughly 50 per cent of global market capitalization, and that's after U.S. markets have outpaced overseas markets in recent years. Passive investors should therefore target a U.S. stock allocation that's closer to, say, 45 per cent.

But what about active investors who want to deviate from market cap based on valuations? We agree that higher valuations augur lower expected returns, and vice versa. We also agree that there's no correlation between valuations and short-term returns, so it's not surprising that investors who bought cheap EAFE and EM stocks in recent years haven't yet been rewarded.

Even so, it seems sensible for investors to tilt their portfolios in favour of cheaper EAFE and EM stocks if they're willing to hang around long enough to realize those stocks' higher expected returns. It's like the choice investors routinely make between stocks and bonds. Stocks have a higher expected return than bonds, but those returns may take a long time to realize, if at all.

The difference is that stocks are inherently riskier than bonds. But if we're right that the difference between U.S. and EAFE valuations is driven by investor psychology, then investors may not be taking more risk in EAFE (or even in EM) from current valuations.

Ritholtz: You just revealed the hidden core of our debate: The U.S. versus overseas markets, using valuation as a deciding factor, is a loosely disguised active-versus-passive debate. I will grant you, U.S. stocks are expensive relative to their history. However, I will lay down these two complicating caveats: We have never had a period that looks like this one. This has been a post-credit crisis recovery with very low rates, practically free capital, almost no inflation, weak wage gains and full employment. Why bring up that laundry list of conditions? The alternative is to try to use a single variable -- are stocks expensive based on earnings? -- to make a buy-sell decision. Sometimes cheap stocks get cheaper and continue to fall; other times expensive stocks get more expensive and keep going up! Whenever I hear the phrase, "this asset class is expensive," I want to know more. Otherwise, that one piece of information is less helpful than most people tend to believe. The bottom line is that U.S. stocks have been selling at a premium for a while. I don't want to abandon U.S. equities, but I would strongly advocate diversifying into MSCI EAFE and MSCI EM indexes. Your grandkids will thank you.

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Nir Kaissar is a Bloomberg Gadfly columnist covering the markets. He is the founder of Unison Advisors, an asset management firm. He has worked as a lawyer at Sullivan & Cromwell and a consultant at Ernst & Young.

Barry Ritholtz is a Bloomberg View columnist. He founded Ritholtz Wealth Management and was chief executive and director of equity research at FusionIQ, a quantitative research firm. He blogs at the Big Picture and is the author of "Bailout Nation: How Greed and Easy Money Corrupted Wall Street and Shook the World Economy."

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