Efficiently Inefficient: How Smart Money Invests & Market Prices Are Determined

Understanding Hedge Funds and Other Smart Money

Hedge funds differ quite a bit from mutual funds.

Unlike mutual funds, hedge funds are largely unregulated and won't necessarily give you your money back when you want it (i.e. you give up liquidity). Hedge funds typically have *much* higher fees in exchange for their much more active money management. This active management (i.e. lots of trades) combined with their typically high leverage, make it so hedge funds are part of a very large proportion of total trading activity.

Finally, in theory, hedge funds returns should be largely independent of the rest of the market - that's one of the primary reasons investors are interested in them. In practice, hedge fund returns typically correlate positively with equity markets.

Some money managers can beat the market when managing small portfolios, but their strategies don't scale, so as new investors flock to these "geniuses", their edge tends towards zero.

Do hedge funds pay off? Some do, at least so long as their genius is relatively unappreciated. Many don't - the attrition rate in the industry is quite high. It's unclear how the "average" hedge fund does relative to the market. It becomes more enlightening to look at the specific strategies rather than talking about hedge funds "in general".

Hedge funds are typically organized in a *master-feeder* structure, where there is one master fund where actual trading takes place, and a number of "feeder funds", which investors actually invest in. The feeder funds will tailor the investment products to the needs of different investors (e.g. different currencies, tax regimes, or risk tolerances). A *management company* hires the employees to make investment decision, conduct trades, and generally manage the fund.

Evaluating Trading Strategies

You returns are often separated into four components: the risk-free rate of return, $\alpha$, $\beta$, and $\gamma$. TODO

$\beta$ is particularly important here because you can make your $\beta$ basically whatever you want for very low fees by longing or shorting index funds. For this reason, it is not impressive for a strategy to have high returns merely through high $\beta$ - it is *only* impressive if those high returns are via high $\alpha$ - an impossibility according to the CAPM model. Typically a fund's "greeks" are estimated from historical data and considered evidence of skill rather than luck if they reject the null hypothesis via a t-test.

Academics often supplement the basic CAPM model by including other $\beta$s. In particular, they frequently include how a stock moves relative to index funds that aren't don't just track the overall market. For instance, you might include an index that goes long on small companies and short on large ones.

Even after these adjustments, using $\alpha$ alone is an imperfect measure of performance, because you can take any positive $\alpha$ and trivially make it arbitrarily large with leverage. To adjust for this, investors use the Sharpe ratio:

The Sharpe ratio, however, doesn't address that $\alpha$ is not simply excess returns, so, instead, the information ratio is typically used:

*This* ratio is immune to manipulation via leveraging the fund or a market index. Often it is re-defined relative to a benchmark:

Many managers use cash as their benchmark, which reduces this to

This measure of performance is controversial since many hedge fund investors don't want to use leverage directly. To address this, investors use the alpha-to-margin ratio:

which effectively computes the return on a maximally leveraged market-neutral strategy (hedge funds are subject to margin requirements that depend on, among other things, how liquid their assets are).

Pedersen discusses a couple other metrics before moving on to the next topic: estimating these metrics using real-world data.

He suggests estimating these metrics using historical data with standard statistical definitions for expected return and variance.

Since returns are roughly independent over time, both returns and variance are proportional to the duration of the time intervals used. For instance, annual returns should have about 12x the expected value and 12x the variance of monthly returns. From this and the Sharpe ratio formula, it follows that the Sharpe ratio grows proportional to the square root of the time period used. For instance, the Sharpe ratio for annual returns is roughly $\sqrt{12}$ larger than the Sharpe ratio for monthly returns.

Conversely, the Sharpe ratio tends towards zero at very small scales, which explains why even very successful strategies will tend to see losses nearly 50% of the time at very small scales.

The high water mark ($HWM$) is the highest price ($P_t$) a hedge fund has achieved. A fund's drawdown ($DD$) is how much the hedge fund is down since its peak:

Large drawdowns are risky because

• of the direct losses
• it causes investors to pull out of the hedge fund
• various necessary parties may increase requirements or pull out of operations all together

For this reason, people sometimes also consider the maximum drawdown over some time period (e.g. X years).

Hedge funds often report returns on a lag. For instance, a hedge fund may report returns a month after they occur. If one does so, their monthly returns will appear independent of stock moves even if they literally just invest in the S&P 500, which will dramatically inflate their estimated $\alpha$. We can account for this by using a regression with multiple lagged $\beta$ parameters:

We can then estimate the true $\beta$ as the sum:

Finding and Backtesting Strategies

There are two classes of reasons for repeatable trading profits. The first is fairly easy to understand: information advantages. This in turn can be divided into three types:

• information production - gathering data, analyzing future prospects, uncovering fraud/misreporting, etc.
• information access - insider trading, calling doctors to ask what medicines they are prescribing, etc.
• arbitrage - in the real world, arbitrage is risky for a variety of reasons, which can allow predictable bias to persist for weeks

The second class of reasons for repeatable trading profits is compensation for liquidity risk. This can also be broken up into three parts.

The first type of liquidity risk is market liquidity risk. During some situations, the bid-ask spread can grow dramatically, preventing you from selling/buying a security. For this reason iliquid securities must offer investors a premium. The liquidity of a security can change over time, so its not just the security's current liquidity that matters - it's also how this liquidity is expected to change both over time and relative to other assets: securities that become iliquid when everything else is becoming iliquid require an especially high premium. Market liquidity risk is typically accounted for by modifying the CAPM model.

The second type of liquidity risk is funding liquidity risk - If you short a volatile stock, there's a chance it will double, forcing you to liquidate before it crashes. Investments like this require higher margin to avoid being forced to "unwind" the position. This makes them less desirable than similarly risk investments. Hence, a portfolio of risky stocks tends to underperform a leveraged portfolio of safer stocks. This can likewise be accounted for with a modification to the CAPM model.

Put succinctly, market liquidity risk is the risk that you cannot sell a security when you want to; funding liquidity risk is the risk you must sell them.

The third type of liquidity risk is demand pressure. This is a kind of catch-all category for "contrarian" trading. For instance:

Other examples of demand pressure include

• Companies desire options in commodity markets to hedge against price change risks.
• Investors desire index options hedge their market risk,
• Some investors must hold bonds with certain ratings, so a rating downgrade can cause a demand pressure to sell.
• Many passive investors in commodities automatically roll their future contracts forward on certain dates determined by the S&P GSCI index, which creates pressure to sell and buy on the contracts on those dates.
• Some securities see a surge in demand for their shares as a result of temporary popularity - particularly companies with direct customer interactions.

Typically, a trading strategy succeeds much more at a backtest than it would now for a number of largely unavoidable reasons:

• You typically generate strategies based on what has worked in the past.
• The market gets more competitive over time.
• You typically do lots of backtesting and then choose the ones that worked best (i.e. multiple hypothesis testing).

Because of these sources of bias (and others discussed below), a strategy succeeding at a backtest doesn't prove it is now good, but a strategy failing at a backtest is quite indicative that it is now bad. Though imperfect, a backtest can also help you discover a strategy's risks and ways to improve it.

A back test needs four components:

• Universe - A set of securities available for trading
• Signals - Raw input data and pipelines for analyzing it.
• Trading Rules - Rules that determine how to trade based on
• Time Lags - Accounting for the fact that you can't trade instantly; it is typical to assume it takes a day or two for a trade to go through.

To help make things more concrete, here are two broad classes of trading rules:

• Enter-exit trading rule - The rule looks at each asset individually and determines when and how much to buy and sell. For example, you might buy $1000 of gold futures if it exceeds its past 20-day highest value and you might sell them if the price drops below its 10-day minimum.
• portfolio rebalance rule - Your rule selects a basket of securities to satisfy certain criteria. For example, you might hold an equal-weighted portfolio of the the 10% cheapest stocks by their book-to-market ratio, rebalancing at the beginning of each month. Note that, unlike a enter-exit trading rule, a portfolio rebalance rule makes it hard to talk about whether any particular trade "worked".

In addition to the unavoidable sources of bias discussed, here are some biases that are typically avoidable with some work:

• You have to choose your basket of securities using information you had at the time. For instance, you can't choose the current S&P 500 to simulate a strategy over the last 20 years, because many bad stocks left the S&P 500 during this time, bad stocks that would be unfairly excluded from your simulation.
• In addition to simple time lags like the above, its important to note that official announcements frequently happen after the even has already occurred (e.g. first-quarter earnings are reported well into the second quarter).
• If you use data over a timeframe to estimate parameters, evaluating the strategy over the same timeframe creates bias due to statistical overfitting.
• You must account for transaction costs.

Finally, a "predictive regression" is a regression where the future return is predicted by the signals you know. At the end of Chapter 3, there is an interesting correspondence theorem by which every predictive regression can be expressed as a "portfolio sort" and vice versa.

Portfolio Construction and Risk Management

After a hedge fund has identified trades that can be expected to make money, the next step is to combine them into an overall portfolio to deliver the best possible risk-adjusted returns. This is a dynamic process as the expected returns and risks, of each strategy can vary over time - not to mention their covariances - this complexity is compounded by the use of leverage and the skittishness of investors.

If you have thousands of positions, it is infeasible to manage risk using raw human skill/intuition, so people typically turn to quantitative methods such as the Markowitz model. TODO: add info form pg 57 to the Markowitz page.

The Markowitz model uses the most common measure of risk: volatility (i.e. the standard deviation of returns). However, in the real world, this does not capture tail-risks well, especially for hedge funds, so other measures are needed. These include

• value-at-risk - the xth percentile return
• expected loss - the expected loss conditioned on a move at least as bad as the xth percentile return
• stress loss - simulate bad historical and (imagined) future events and determine the largest loss the strategy would've had

To control risk, hedge funds will have rules limiting how much risk a fund, asset class, or strategy is allowed to take; some will also have a risk target that they tend to gravitate towards in the long-run.

In addition to these proactive attempts at risk management, hedge funds will also have mechanisms that react to market conditions as they occur by adjusting leverage and held positions to reduce risk exposure. Conversely, when markets recover, they specify how quickly to take on new risk. These plans are particularly important because the alternative is typically to trade on emotions during difficult periods.

Trading and Financing a Strategy

Investment strategies have two main sources of costs: transactions and leverage.

Transaction costs include not only explicit commission costs, but also the implicit cost of the bid-ask spread (and, for very large investors, "market impact" costs - i.e. when *you* cause the market price to change). Some costs scale with the number of trades, while others scale with the total volume traded, which affects how frequently a strategy can profitably trade.

Empirically, US stocks have typical transaction costs around 0.07% but these costs rise dramatically if you trade more than ~10% of a stock's typical daily volume because at that point you start to significantly affect a stock's price. This is one of the main reasons trading strategies (and hedge funds) typically have limited scaling ability.

In addition to the literal transaction costs, there is additional opportunity cost: transaction costs cause the truly optimal strategy to lag behind the hypothetical optimal strategy, which makes you miss out on potential profits. Both these costs combine to form your "implementation shortfall". Whether you should be trading more quickly or slowly largely can be found by decomposing these two sources of transaction costs.

Besides transaction costs, the other main cost with funding an investment strategy is leverage, which likewise also include both an explicit cost (interest) and an implicit cost (see "funding liquidity risk" discussed above).

There are three measures of leverage:

where NAV is your net asset value.

The reason long and short positions are considered separately is that the latter are typically a hedge against risk. Since leverage is typically used as a measure of riskiness, it is odd to treat them like long positions.

Hedge funds get cash to invest from several different sources:

• Cash given to them by investors
• Borrowing money to buy securities and use those securities as collateral
• Shorting securities and using the resulting cash
• Implicit leverage from investment in derivatives
• "Repos" Repurchase agreement. In Wikipedia are used to cover short-term (i.e. daily) operations.

The funding liquidity risk inherent in this leverage becomes particularly bad during liquidity spirals, whereby a price drop, causes investors to sell/unwind, which causes a further price drop.

While during normal conditions, prices are driven by fundamentals, during liquidity spirals, prices are driven by these forced and unforced sell-offs. This creates a complete change in conditions whereby normal security correlations can change, with unrelated securities starting to move in tandem.

This is exacerbated by a couple issues:

• Hedge funds are typically both the investors unwinding during these times and also the normal providers of liquidity.
• Some investors exploit or even induce these liquidity spirals (e.g. "short squeeze" Short squeeze. In Wikipedia), though this can be difficult to ever know or prove since such actions are very similar to the actions of investors trying to protect themselves against those very same spirals!

Introduction to Equity Valuation and Investing

A stock's intrinsic ("fundamental") value is its time-discounted net cash flow (typically dividends and buy-backs). Value investors try to identify stocks whose intrinsic value is higher than their market price. However, for a variety of reasons, prices can wander from their fundamental values - especially in stocks that are illiquid, volatile, or costly to short-sell.

Time discounting isn't always a straightforward as in textbooks: a stock's discount rate depends on the risk-free rate, the market risk premium, and the individual stock's $\beta$ - all parameters that can change over time.

One popular model is Gordon's Growth Model which assumes a constant discount rate ($k$) and a constant dividend growth rate ($g$). This results in a very simple formula for computing intrinsic value:

Other models and accompanying themes and various exist in this space. In particular, some investors place more emphasis on a stock's net income under the assumption that a dollar reinvested is as good as dollar paid out in dividends.

Discretionary Equity Investing

Estimating a stock's future dividends depends on a large number of factors, some quantitative others less so. For this reason, most value investors use a "margin of safety" whereby they only buy stocks when their estimate of their fundamental value is sufficiently below the market price.

I encourage you to read the book for more information.

Dedicated Short Bias

Suppose WMT is trading at \$100, that Alice owns one share, and that Bob wants to short it. Bob borrows the share from Alice, promising to give it back the next day. Bob sells the stock for \$100. If the stock falls to \$98 the next day, Bob buys it back, returns it to Alice, and pockets the \$2 as profit.

This glosses over some details:

• Bob will have to give Alice a "loan fee". In practice, these fees are usually quite small because (a) lending out her share for a day doesn't materially affect Alice's portfolio, and (b) the same individual share can be shorted multiple times.
• Bob can not use the $100 he gets from selling WMT to invest in other positions, because he needs to use it as collateral in case WMT doesn't fall. In fact, Bob has to put up additional collateral in case WMT increases in price.
• If Bob wants to short for multiple days, he can "roll over" his short positions each day. However, there is a risk that the lender will refuse to lend again. This happens, presumably, when a stock is at risk of rapidly appreciating in price, so in these instances it can be difficult for Bob to find an alternative lender. When this happens across the market, it's called a "short squeeze."
• Finally, shorting a stock that goes up by less than the overall market has positive alpha in principle, but is a losing trade in isolation.

Without short-selling, WMT's price is determined only by the optimists - as the pessimists simply hold 0 stock in WMT and invest in other things. Pedersen provides a neat example of how two sets of investors with different expectations can lead to a bubble in such a situation (see "Speculative Bubbles: An Example").

Shorting a stock effectively increases the supply of shares, which drives prices down. In this way, the ability to short prevents bubbles and makes markets more liquid.

Quantitative Equity Investing

Quantitative equity investing is about using models and algorithms and can be divided into three types of trades:

• fundamental quant - apply fundamental analysis (like "normal" discretionary traders) but in a systematic way. Pedersen takes this opportunity to talk about some general heuristics that have worked historically:
• Value investing - e.g. stocks with high book to market ratios (BM) tend to outperform stocks low BM
• Momentum investing - e.g. stocks that have gone up the most over the last 12 months tend to outperform during the subsequent month
• Quality investing - todo
• Betting Against Beta - in practice, leveraging low-beta stocks outperforms buying high-beta stocks for the same amount of risk
Quants can models to eliminate various types of risk (market risk, industry risk, etc.) until they only have the risk they want to bet on (e.g. the risk of implementing a momentum strategy).
• statistical arbitrage - exploit relative mispricings between closely related stocks. This includes stocks that should be priced identically ("Dual-Listed shares") or are shares of different classes (e.g. voting v non-voting). Many non-zero spreads persist in the economy, particularly when one share is more liquid than other - providing clear evidence against the EMH and evidence in favor of this book's thesis. Other more complex strategies fall in this category as well
• high-frequency trading (HFT) - trading based on statistics and information processing, with a focus on speed. In addition to liquidity-providing strategies (mentioned in the beginning), HFT also institute various other strategies including those similar to statistical arbitrage and strategies that attempt to take advantage of other HFT strategies (i.e. taking advantage of limit orders before they're canceled).

I strongly encourage reading the sections titled "The Quant Event of 2007" and "The Flash Crash of 2010" for a fascinating narrative of how quant trading strategies can create feedback loops that drive short-term market crashes.

Introduction to Asset Allocation

There are several strategic allocation strategies. Some common ones are

• Passive - you allocate assets according to the market capitalization of each market
• Constant Rebalanced - a portfolio that regularly rebalances so that each asset class is a certain percent of the overall portfolio
• Liquidity-Based - certain investors need to be able to exit positions quickly (e.g. to cover leverage risk) and so have to avoid certain illiquid assets
• Risk-Parity - Set asset allocations such that each class contributes equally to portfolio risk

Asset allocation targets can be changed in the short-run too. For instance, it is known that periods with high dividend yields have historically predicted periods of high stock returns relative to the risk-free interest rate. For this reason, during such periods investors might put more of their portfolio in stocks. This conclusion depends, of course, on whether you think this relationship was and continues to be real - or whether it was a statistical or historical fluke.

Stock returns are frequently broken down into four components:

Specifically

• Dividend Yield - dividends this year divided by the starting price - historically about 3.9%
• Dividend Growth - percent change in dividends from last year - historically about 1.6% after adjusting for inflation
• Valuation Change - percent change in the Price-Dividend ratio - historically about 2.4% but 0 in the long-run
• Small Adjustment - a second-order term for when dividends grow and the PE ratio changes at the same time - historically about 0.15%

This all suggest that while gains averaged around 8.1% in real terms between 1926 and 2013, future returns will likely be much lower.

Alternatively, returns can be decomposed into the "earnings yield" (net earnings divided by market cap) and "price surplus", which is defined as the difference between the earnings yield and the rate of return. In the long-run, the expected "price surplus" is just the inflation rate. For this reason, expected earnings can be viewed as a measure of expected real returns.

Bonds are more straightforward: if you assume you reinvest the interest payments, a bond that pays 5% of the principle each year has a rate of return of 5% if held to maturity. Things only get a little more complicated if you sell before the bond reaches maturity.

The difference in the interest on a corporate bond and a government bond is called the "credit spread". In general, both investment-grade and speculative-grade bonds have credit spreads much larger than their long-term default losses.

The chapter closes with a discussion of investing in foreign currencies.

Global Macro Investing

A "carry trade" is when you borrow money in a currency with low interest rates to invest in a currency with high interest rates, pocketing the difference if exchange rates don't change.

Economists used to believe the expected exchange-rate change must equal the different in interest rates, but abundant historical data has disabused them of this notion. That being said, carry trades often have large tail risk.

In addition to exchange rates, global macro traders obsess over central banks since (a) their actions move asset prices and (b) they are not profit maximizers. For instance, if you expect the central bank to raise rates, you would short bonds. From here, Pedersen enters a brief introduction to macroeconomics, which I am skipping here.

Global macro traders also care about international trade, politics, regulatory uncertainty, etc. To a large degree the strategies that work within a country work between them (e.g. momentum trading).

Managed Futures

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