**"risk premium"**

## Hedge Fund Strategies (10) – Trading the TED Spread

*by Eric Bank on October 2, 2011 · No Comments · in Documenting the Search for Alpha*

The difference between the interest rate on three-month Treasury bills versus the three-month London Inter-Bank Offering Rate (LIBOR), is known as the TED spread.

The difference between the interest rate on three-month* Treasury bills* versus the three-month ** London Inter-Bank Offering Rate (LIBOR)**, is known as the

**. The term “TED” arises from the 90 day**

*TED spread***-bills and 90 Eurodollar (**

*T***certificates of deposit. TED-based strategies can be viewed as credit spread trades, pitting highest quality government debt against slightly lower quality AA-rated inter-bank debt.**

*ED)*The TED spread is measured in ** basis points** (bps) where 100 basis points = 1%. For example, if LIBOR is 4.50% and 3-month T-Bills are trading at 4.10%, the TED spread would be 40 bp. The historic range of the spread has hovered between 10 and 50 bps, except during financial panics or downturns.

Recalling our discussion of the Capital Asset Pricing Model (CAPM), the risk-free rate is used as the basis for finding an asset’s or portfolio’s risk-premium. Well, that risk-free rate is none other than the 3-month T-bill rate – the “T” in TED. LIBOR is by definition riskier, because it has more than zero risk that one of the counterparties to an inter-bank load will default. Therefore, when the TED spread increases, investors are more concerned about counterparty risk, and thus demand a higher LIBOR (or equivalently, a lower price on Eurodollar securities) to induce them to assume the perceived extra risk. Conversely, the TED spread decreases when credit conditions are considered benign.

TED is an ** inter-commodity spread **- you can trade the TED spread by pairs-trading T-bills and Eurodollar CD’s, or more likely, the corresponding futures contracts. If a hedge fund manager feels that credit conditions are going to worsen, he goes long the TED spread by shorting ED futures and buying T-Bills futures. The reverse trade, a short spread, favors the optimistic point of view regarding credit conditions, causing the spread to decrease.

You can also trade so-called ** term TED spreads**, which use longer-maturity (i.e. 6 month, 9 month, etc) securities.

During the financial meltdown of 2008, the TED spread hit a record 465 bps, presaging the collapse of the interbank lending markets. Only massive injections of liquidity from central banks avoided a complete cratering of the financial system. The tendency of such liquidity injections during times of financial crises tends to moderate the long-term volatility of the TED spread.

In our next blog, we’ll examine liquidity-based yield spreads.

## Yield Curve – Structure

*by Eric Bank on May 2, 2011 · No Comments · in Documenting the Search for Alpha*

Yield curves (also known as the term structure of interest rates) plot debt maturities (the independent variable) against interest rates (the dependent variable).

Loyal readers know that we are currently surveying hedge fund strategies. As we pivot from equity strategies to fixed-income arbitrage, we will first take a short “time out” to learn about ** yield curves**. In this article we’ll discuss yield curve shapes; next time out we will explore the theories that attempt to explain yield curve behavior.

Yield curves (also known as the ** term structure of interest rates**) plot

**(the independent variable) against**

*debt maturities***(the dependent variable). Debt maturities indicate the length of the borrowing period for a debt instrument. The interest rate associated with a given borrowing period is a point on the yield curve. Curve segments between actual maturities are interpolated. Yield curves are specific for a given currency – the yield curves for U.S. dollar-denominated Treasury bonds will (almost always) differ from the analogous chart of U.K. pound-denominated gilts.**

*interest rates*Debt yield is the overall rate of return on a debt instrument. Debt that is “locked up”, as in a certificate of deposit, will usually offer a higher yield than an on-demand savings account, due to the higher certainty of holding the former to maturity. Yield curves normally ascend with time, but the *rate of increase *diminishes with increased time. The fancy phrase for this is an ** asymptotically upward slope**. It reflects the fact that it is riskier to hold longer maturities, because it’s harder to predict distant future interest rates than it is to predict near term interest rate. This increased uncertainty usually demands a

*risk premium*, i.e. a higher interest rate (known as a

**). This makes the most sense if investors anticipate a period rising short-term interest rates – current investors willing to tie up their money today must be compensated for forgoing higher interest rates tomorrow. But even if rates are not forecast to rise, the liquidity spread tends to give longer maturities higher yields.**

*liquidity spread*An ** inverted yield curve** is, as you might suspect, one in which short term rates are higher than long term ones. Inverted curves indicate an anticipated drop in interest rates over time. This is not considered a good thing – inverted yield curves are often associated with strong recessions and depressions. Forecasts of a weak economy motivate long-term investors to agree to lower yields, on the premise that yields may go even lower. On the plus side, inverted yield curves indicate a belief in low future inflation. However, in an economic panic, a

**may increase demand for, and thus lower the yield of, long-term government bonds.**

*flight to quality*Currency is a prime determinant of yield curve shape. Another determinant is the type of debt instrument: government bonds, bank debt, corporate bonds, and asset-backed securities. The latter three also vary by the creditworthiness of the issuer – debt with ratings of Aa/AA and above is less risky than lower-rated debt, and hence demands less of a premium over the interest rates for government debt. The ** London Interbank Offered Rate (LIBOR)** is a benchmark rate reflecting the interest rates top London banks charge each other for unsecured funds. LIBOR is important in the swap market because it is used to peg the floating rate leg of an interest rate swap. For this reason, the LIBOR yield curve is often referred to as the

**.**

*swap curve*As we noted, the normal yield curve has a positive slope, reflecting investor sentiment that economies will grow over time and that inflation rates will rise accordingly. Central banks, such as the U.S. Federal Reserve, control a country’s money supply in order to either keep a lid on inflation (by tightening the money supply, i.e. raising short term interest rates) or fight recession and deflation (by increasing liquidity and reserves in credit markets, i.e. lowering short term rates and/or printing more money).

Historically, the 20-year Treasury bond has yielded a ** spread** of two additional interest rate points above the three month Treasury bill. However, events can cause yield curves to steepen (larger spreads) or flatten (smaller spreads). Recently, the spread between 2-year and 10-year Treasuries widened to record-setting amounts approaching 3%. Sometimes, a yield curve is bicameral, or humped, meaning that medium-term yields exceed long- and short-term ones. This can occur when short term volatility is expected to be more significant than that in the long term. Flat yield curves can predicts steady interest rates or reflect general uncertainty about the economic future.

## Hedge Fund Strategies – Long/Short Equity Hedging

*by Eric Bank on March 28, 2011 · No Comments · in Documenting the Search for Alpha*

A long/short equity hedging strategy consists of selecting a core long equity portfolio and then partially or fully offsetting it with short equity positions.

A long/short equity hedging strategy consists of selecting a core long equity portfolio and then partially or fully offsetting it with short equity positions. The goal is garner returns that resemble those available from a long call option – upside exposure and downside protection. The short equity positions may take the form of short stock positions, short call/long put options, and short futures/forwards, among others.

Most practitioners of long/short equity hedging tend towards a directional long bias – they do not completely hedge their long positions. Of course, in difficult market conditions, this bias may disappear or be reversed. Different styles of investing (such as ones based upon geography, sector, capitalization, book value, etc.) can overlay this strategy. So, for instance, a long/short portfolio may be long “undervalued” stocks or stocks from neglected countries or sectors, and short “overvalued” stocks from popular regions or sectors. Of course, notions of valuation are in the eyes of a fund manager, but there is a general consensus that, for instance, small-cap stocks are systematically undervalued, and hence provide a risk premium (in the case of small-cap stocks, the risk premium is often called a liquidity premium), relative to large-cap stocks. Another example of systematic risk premia involves so-called “value” stocks, as opposed to “growth” stocks. Thus, a typical long/short portfolio may be long small-cap and/or value stocks, and short large-cap/growth stocks (or equivalent short positions in indexes or derivative instruments).

There are many other ways to target undervalued stocks using fundamental analysis in either a top-down or bottom-up approach. Top-down analysis involves identifying socio-economic trends, and then sectors and companies that will benefit therefrom. Bottom-up stock selection rests on the information gleamed from a company’s financial statements, SEC filings, and various external reports (research reports, news articles, personal interviews, trade shows, etc.). In either approach, fund managers may be free to put on positions as they see fit – there need not be any benchmark portfolios associated with a long/short strategy. Thus, managers using this strategy can be unencumbered with the potential drag of trying to outperform a benchmark portfolio.

So, how much does a manager’s superior skill (alpha) contribute to returns from a long/short hedge fund? We have seen that built-in systematic risk premia (beta) can be a significant source of return, as in small-cap or value-based positions. Studies have indicated that up to 70% of returns from this strategy are a result of market exposure. The fact that the strategy works much better in strong up-markets than in flat or bear markets reinforces the perception that much of the return reaped by hedge funds utilizing a long/short strategy arises from beta, and that the added kick provided by alpha may be over-hyped.

A recently-popular variation on the long/short strategy is known as the “enhanced active 100X –X” strategy. A hedge fund manager allocates a percentage of his/her book, say 30%, to short positions, and then, through the use of prime brokerage leverage techniques uniquely available to hedge funds, uses the proceeds from the short sales to put on a long position equaling 100% plus the amount shorted – in this case giving a total long position of 130%. This example would be called an active 130-30 strategy. Quantitative techniques are often used in this variation; as such, it might be termed a hybrid of long/short equity hedging and equity hedged market neutral investing. Before we turn to the latter strategy, we’ll continue next time with an in-depth review of enhanced active 100X-X investing.

## Consumption CAPM

*by Eric Bank on March 13, 2011 · No Comments · in Documenting the Search for Alpha*

When we recently examined Intertemporal Capital Asset Pricing Model (I-CAPM), we understood it to be an extension of CAPM in which investors establish additional portfolios to hedge specific risks representing short-term idiosyncratic tastes and preferences. Typical examples of these specific risks include inflation, job loss, economic downturn, etc. The model is somewhat incomplete, in that it doesn’t specify how to arrive at the proper factors to quantify these additional hedges. Another approach, called the Consumption CAPM (C-CAPM) posits a single additional hedge portfolio based on consumption risk, which is a hedge against future consumption rates.

When we recently examined **Intertemporal Capital Asset Pricing Model (I-CAPM),** we understood it to be an extension of CAPM in which investors establish additional portfolios to hedge specific risks representing short-term idiosyncratic tastes and preferences. Typical examples of these specific risks include inflation, job loss, economic downturn, etc. The model is somewhat incomplete, in that it doesn’t specify how to arrive at the proper factors to quantify these additional hedges. Another approach, called the **Consumption CAPM (C-CAPM)** posits a single additional hedge portfolio based on** consumption risk**, which is a hedge against future consumption rates. Let’s see how that works.

C-CAPM assumes that investors are not interested in maximizing their portfolio, but rather in *maximizing over their lifetimes the consumption they get from their portfolio*. Therefore, there is a tradeoff between current and future consumption. The model assumes that investors will sell assets during bad economic times and buy them when times are good. That means that, say, a yacht, will have to have a very high future expected return (a high risk premium) to induce the owner to hold onto it when times are bad. Therefore the systematic risk of the asset (the yacht) is tied to the state of the economy.

An illustration will clarify.

Each person has their own set of **utility functions**. For instance, if I buy an asset (such as a yacht) today, it will cost me $X. If I am to hold off on buying the asset, it had better be worth it to me to wait. In other words, I should receive a return on the amount, $X, that I didn’t consume today. If that return, which we’ll call the consumption premium, is high enough, I’ll wait; if not, I’ll buy the asset today. At some rate of return (let’s call it r_{0}) I am indifferent to waiting or consuming. If my return on $X is expected to exceed r_{0}, I’ll wait. If it is expected to be less than r_{0}, I’ll consume today.

Now, if I expect a rosy economic future, I will assign a *higher* risk premium to the yacht; conversely, if I see the future economy tanking, I *lower* risk premium on the yacht, making it more likely to consume the asset now rather than waiting. Of course, if I’m anticipating a severe depression, I just might keep the $X in Treasury bonds and adjust my utility function accordingly. Since the price of my current Treasury bonds will rise during a depression (because of their relatively high interest rates), they are a good hedge against bad times – something that cannot be said about a yacht. In terms of C-CAPM theory, the returns on the Treasury bonds have a *negative correlation* with consumption, and are thus are worth more during times of depressed consumption. The yacht’s returns have a *positive correlation* with consumption (yachts sell for more in times of consumption growth), and are therefore worth less during low-consumption periods.

Bottom line: hedge your portfolio with assets that will do well when economic consumption rates drop.

In C-CAPM, one has to measure the consumption premium accurately in order to have a valuable model. One problem that arises is that of **satisfice**: are consumers really looking to optimize consumption, or are they merely satisfied with achieving some minimum constraint? This will have considerable impact on the rate at which future consumption is discounted to arrive at its value today.

Now that we’ve looked at CAPM and several alternatives, we want to next explore the topic of specific **risk premia**, which we’ll loosely define as the return (above the risk-free rate) that can be associated with taking on certain systematic risks. We want to see whether, for any given hedge fund strategy, returns can be ascribed solely to the systematic risks (i.e. **beta**) of the strategy, or whether some portion of the return is due to a superior fund manager (**alpha**). This will lead to our ultimate topic: **hedge fund replication**.

## Arbitrage Pricing Theory – Part Two

*by Eric Bank on February 10, 2011 · No Comments · in Documenting the Search for Alpha*

Arbitrage Pricing Theory (APT) is a multi-factor model in which a series of input variables, such as macroeconomic indicators and market indices, are each assigned their own betas to determine the expected return of a target asset.

In our previous blog on this subject, we identified **Arbitrage Pricing Theory (APT)** as a* multi-factor model* in which a series of input variables, such as macroeconomic indicators and market indices, are each assigned their own *betas* to determine the expected return of a target asset. Recall from its equation that the expected return of an asset *i *is a linear function of the assets’ betas to the *n* factors:

E(r_{i}) = R_{f} +b_{i1} RP_{1}+. . .+b_{in} RP_{n} where

- RP
_{n}is the premium on factor n - b
_{in}is asset i’s loading of factor n - R
_{f}is the risk-free rate

Let’s explore the theory in a little more depth. It is based on the concept of arbitrage, which is when a trader makes a risk-free profit when a single asset is priced differently in different markets. By shorting the higher price while simultaneously buying at the lower price, the price differential is locked in. Unfortunately, in today’s lightning-fast global markets, this is a very rare opportunity.

The theoretical value of the APT is its ability to detect a *mispriced asset*: if the weighted sum of each factor’s risk premium is different from the asset’s current risk premium (as indicated by the asset price), then an arbitrage opportunity exists. If you think as the expected return on an asset as a *discount rate* on its future cash flows, a price can be calculated and compared to the actual current price.

We use the term asset here to encompass both single assets and portfolios. If a single asset is being modeled, then the asset is exposed to each macroeconomic factor to the extent of its beta with that factor. Let’s assume we identify a mispriced asset based on a 5-factor ABT model. An *equivalent portfolio* would contain a set of 6 correctly-priced assets, one asset per factor plus one extra. Each asset would have the same exposure to a single factor as the mispriced asset. By varying the amount of each asset in the portfolio, you can arrive at a portfolio beta/factor that is the same as that for the mispriced asset. You can now treat the portfolio as a *synthetic* version of the asset, and take a short or long position in the portfolio to offset the opposite position in the mispriced asset, theoretically capturing a risk-free profit.

Of course, identifying the important factors associated with a particular asset is no small undertaking, and APT does not offer a roadmap. However in general, one would have to take into account, for each of the factors affecting a particular asset, the expected return of each factor and the asset’s sensitivity to the factor.

We’ll complete our look at APT next time by comparing it to the Capital Asset Pricing Model.

## Arbitrage Pricing Theory – Part One

*by Eric Bank on February 5, 2011 · No Comments · in Documenting the Search for Alpha*

Arbitrage Pricing Theory (APT) is a multi-factor model conceived by Stephen Ross in 1976. It is a linear equation in which a series of input variables, such as economic indicators and market indices, are each assigned their own betas to determine the expected return of a target asset. These factor-specific betas (b) fine-tune the sensitivity of the target asset’s rate of return to the particular factor.

Last time out, I promised we would look at the risk premia associated with various hedge fund strategies. But first I’d like to finish the discussion of pricing models that we began with our look at the **Capital Asset Pricing Model**.

**Arbitrage Pricing Theory (APT)** is a* multi-factor model *conceived by Stephen Ross in 1976. It is a linear equation in which a series of input variables, such as economic indicators and market indices, are each assigned their own *betas* to determine the expected return of a target asset. These factor-specific betas (b) fine-tune the sensitivity of the target asset’s rate of return to the particular factor. Here are the equations:

Suppose that asset returns are driven by a few (*i*) common systematic factors plus non-systematic noise:

r_{i}= E(r_{i}) +b_{i}_{1} F_{1} + b_{i}_{2} F_{2} +· · ·+b_{in} F_{n} + ε_{i}_{ } for i = 1, 2, . . .n where:

- E(r
_{i})*i* - F
_{1}, . . ., F_{n}are the latest data on common systematic factors driving all asset returns - b
_{in}gives how sensitive the return on asset i with respect to news on the n-th factor (*factor loading*) - ε
_{i}is the idiosyncratic noise component in asset i’s return that is unrelated to other asset returns; it has a mean of zero

APT claims that for an arbitrary asset, its expected return depends only on its *factor exposure*:

If we define RP_{i} = the *risk premium *on factor i = the return from factor i above the risk-free rate = (rF_{n}−R_{f}), then the **APT equation** is:

E(r_{i}) = R_{f} +b_{i1} RP_{1}+. . .+b_{in} RP_{n} where

- RP
_{n}is the premium on factor n - b
_{in}is asset i’s loading of factor n - R
_{f}is the risk-free rate

So you can see, the expected return of an asset *i *is a linear function of the assets’ betas to the *n* factors. This equation assumes ideal markets and no surplus of the number of factors above the number of assets.

In Part Two, we’ll explore the assumptions and implications of the APT equation.

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