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Expected Return Frameworks

Before valuing cash flows, you must establish the discount rate — the required rate of return that compensates you for the systematic risk of the asset.

The Capital Asset Pricing Model (CAPM) The Capital Asset Pricing Model (CAPM) formalizes the risk-return relationship for public equities, asserting that investors are compensated only for systematic, non-diversifiable risk (market risk). The required rate of return $E (R_{i})$ for a stock is:

E (R_{i}) = R_{f} + β_{i} (E (R_{m}) - R_{f})

where:

The risk-free rate, anchored to the current yield of short-term U.S. Treasury bills (T-bills), which represents a nominal yield with zero credit risk. For daily statistics, refer to the Treasury’s Daily Treasury Bill Rates.
The asset’s beta, measuring the covariance of the stock’s returns with the broad market relative to the market’s variance:
$β_{i} = \frac{Covariance (R_{i}, R_{m})}{Variance (R_{m})}$
The equity risk premium (ERP), representing the excess return demanded by investors to hold the risky market portfolio instead of risk-free assets. Historically, the U.S. ERP has averaged 4% to 6% above Treasuries.

Under CAPM, idiosyncratic (unsystematic) risk is ignored because a rational investor can diversify it away at zero cost. If a stock’s expected return exceeds its CAPM-derived required rate of return, the security is considered undervalued. One computation, because this $r$ feeds every valuation model in the rest of this section: with T-bills at 4%, a 5% ERP, and a stock carrying a beta of 1.2, the required return is $4 % + 1.2 \times 5 % = 10 %$ — and that 10% is the discount rate you would carry into the DDM, the DCF, and the cost-of-equity leg of the WACC below. A defensive name at beta 0.7 prices off $4 % + 0.7 \times 5 % = 7.5 %$ ; the 2.5-point gap between the two discount rates moves a Gordon-model valuation by more than a third, which is why the beta estimate deserves more scrutiny than it usually gets.

Beyond CAPM: Multi-Factor Models Empirical research has demonstrated that CAPM’s single-beta framework fails to explain a significant portion of historical stock returns. To address this, Eugene Fama and Kenneth French developed the Fama–French Three-Factor Model (1992),¹¹⁸ which adds size and value risk factors:

E (R_{i}) = R_{f} + β_{i, 1} (E (R_{m}) - R_{f}) + β_{i, 2} (SMB) + β_{i, 3} (HML)

where:

SMB (Small Minus Big): Captures the size premium — the historical tendency of small-cap equities to outperform large-caps over long horizons.
HML (High Minus Low): Captures the value premium — the outperformance of value stocks (high book-to-market ratio) over growth stocks (low book-to-market ratio).

In 2014, Fama and French expanded the framework to a Five-Factor Model,¹¹⁹ incorporating:

RMW (Robust Minus Weak): Captures the quality/profitability premium, showing that firms with high operating profitability generate superior returns.
CMA (Conservative Minus Aggressive): Captures the investment premium, showing that firms that allocate capital conservatively (low asset growth) outperform those that invest aggressively.

How much of this should you believe? The factor literature is the most rigorously studied corner of finance and also the most heavily marketed, and the marketing has run well ahead of the evidence. Three findings deserve as much weight as the models above.

The premiums shrink once they are published.: McLean and Pontiff tracked 97 published return predictors and found portfolio returns 26% lower out of sample and 58% lower after publication.¹²⁰ Roughly half the decay is ordinary statistical overfitting revealed by fresh data; the other half is capital arriving to trade the anomaly. Either way, the historical premium in the backtest is not the premium available to you now, and any fund pitching a factor is by construction pitching one that has already been published.
The zoo is mostly noise.: Harvey, Liu, and Zhu counted more than 300 published factors and argued that with that much searching the conventional $t$ -statistic of 2.0 is far too low a bar — they propose roughly 3.0 — and that between a third and a half of the published cross-section is likely false positive.¹²¹ Size and value have been examined longest and survive best; the further down the list you go, the more you are buying somebody’s regression.
You cannot live long enough to know.: This is the one that should govern your behavior. Factor returns are so volatile relative to their means that distinguishing a live premium from a dead one takes many decades of data. When value posted the worst drawdown in its recorded history through 2020, Arnott, Harvey, Kalesnik, and Linnainmaa showed the stretch was still statistically indistinguishable from noise¹²² — the data could not tell a dead factor from an unlucky one. Read that as a statement about your empirical evidence, not the factor itself: if the premium stopped existing the year you bought the fund, you would finish your investing life without ever being able to prove it.

The practical conclusion is neither “factors are fake” nor “tilt aggressively.” It is that a factor tilt is a bet you cannot evaluate within your own lifetime, so size it as one: a deliberate minority of the equity sleeve, in a cheap and transparent vehicle, chosen because you accept a decade or more of tracking error against the market without abandoning it. Investors who tilt and then capitulate after five bad years have manufactured the worst version of both strategies. Note also what the tilt costs before it earns anything — higher expense ratios and turnover than a total-market fund, and in a taxable account the distributions that turnover produces (section “Tax-loss harvesting”). The factor has to beat the market by enough to cover that before a single basis point reaches you.

Why premiums decay: markets as ecology. There is a coherent framework behind the decay finding, and it is worth having because it predicts what happens next. Andrew Lo’s adaptive market hypothesis argues that the efficient-market picture borrows the wrong metaphor¹²³ — markets are not a physical system relaxing toward equilibrium under fixed laws, but an ecology of competing participants adapting at different speeds. Strategies are species. A premium exists because some population is behaving in a way that leaves money on the table; it persists while that behaviour persists; it erodes as capital learns. Investors who look irrational are usually running a heuristic that worked in the previous environment — Lo’s image is a shark stranded on a beach, thrashing in the way that used to produce forward motion.

The reason to bother with a metaphor is that it changes what you expect. Under strict efficiency, either a premium is compensation for risk and lasts forever, or it never existed. Under the adaptive view, premiums are born, crowd, and die — which is exactly the McLean-Pontiff result above, and it tells you that a factor’s forty-year backtest is a description of an environment that no longer contains the same participants. It is also the strongest available argument for the market portfolio: if you cannot know which strategies are currently adapted, own the aggregate of all of them and stop paying for the search.

The volatility-timing temptation. Lo’s own proposal is a “dynamic” index fund that shifts to cash when measured volatility crosses a threshold and levers up when it falls, offered with a backtest showing a dollar from 1926 growing to many multiples of the buy-and-hold result. Treat that number the way you would treat any strategy discovered in the data it is tested on. The underlying academic finding is real: Moreira and Muir showed that scaling exposure inversely to recent realized volatility raised Sharpe ratios across many factors.¹²⁴ But Cederburg, O’Doherty, Wang, and Yan re-examined it across 103 strategies and found the implied trading rules are not implementable in real time — reasonable out-of-sample versions generally earned lower risk-adjusted returns than simply holding the unmanaged portfolio, because the relationships the rule depends on are not stable.¹²⁵ Add the turnover, the short-term capital gains in a taxable account, and the certainty that you will be in cash for at least one violent recovery, and the retail version of this idea is market timing with a volatility estimate standing in for a hunch. Volatility clusters, which is why the backtests work; it does not announce direction, which is why the funds do not.

The Buffett case, demystified. The strongest apparent counterexample to indexing turns out to be a factor story. Frazzini, Kabiller, and Pedersen decomposed Berkshire Hathaway’s record and found it largely explained by persistent exposure to cheap, safe, high-quality stocks — essentially value plus quality plus low beta — levered roughly 1.6 to 1 with unusually cheap and patient financing from insurance float.¹²⁶ That is not a debunking; sustaining those exposures through five decades of drawdowns without being forced to unwind is the achievement, and the float is a funding advantage no retail investor has. But it does dispose of the idea that his record is evidence you should be picking stocks. What it is evidence for is leverage you cannot be margin called on, applied to boring companies, held for a very long time.

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