Lecture 4
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Terry Leitch
Copyright © 2018 T Leitch & J Liew
Agenda
- Global Macro
- Discretionary Manager Example
- Fundamental Models
- 4 Known FX Factors
- FX Manager Index
- FX Managers
- Fama French 3 Factor
Discretionary Global Macro
In my opinion, (discretionary) Global Macro is the hardest strategy to properly evaluate. Discretionary managers typically have thematic approaches to their investment process and express their views through a variety of instrument such as futures, options, and fx, across global markets.
Rethink Captilism
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Background: Pound was in the Europe’s ERM, Soros bet that the Pound could not remain within the system, his position made $1B on Sept. 16th, 1992 (short the GBP)
News on 9/17/1992
Global Macro Defined
- The most “flexible” investing process employing economic judgment to justify (huge) positions betting on short-term and long-term movements across global markets
- Managers tend to look for global dislocations employing “macro”-judgment in the attempt to capitalize on both expected and unexpected shifts across the “global” markets
- Some inputs:
- Judgment
- Behavior Finance (Over-/under-reactions)
- Global trade imbalances
- Business cycles
- Geo-political concerns
- Emerging economies
- Risk-based dynamics
- Energy and alternative sources
- Demography
Case Study: Discretionary Macro Hedge Funds
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Ex-PayPal’s Peter Thiel’s hedge fund Clarium captured: (1) USD dollar weakening in 2003, and (2) energy rally in 2005
Best and Worst Environments
Fundamental Models: Yardeni
Fundamental Models: FX Classics and Carry
FX Market Background
- Largest financial market, trades $4T (USD) per day
- Established in 1971, inter-bank or inter-dealer network
- Over-the-counter (OTC), transactions not conducted on exchange (i.e. not like NYSE/Arca, CBOE, CME, etc.)
- Largest volume of trading: London, England
- Other trading centers: New York, Tokyo, Zurich, Frankfurt, Hong Kong, Paris, and Sydney
- Trades 24 hours per day, 5 days per week
- No “inside information”
- Forex traded by: Consumers/Travelers(purchase foreign good/services), Businesses (repatriate exported-sales), Investors and Speculators (hedge funds), Commercial and Investment Banks (deposits/lending and prop), Governments and Central Banks (adjust to financial imbalances)
Good Resource: http://www.oanda.com/
FX Trader’s View
“EURUSD trades ½ pip wide, with $2M on ask and $4M on bid side.”
Buy EUR or “lift the offer” : Buy $1M EUR and sell $1,348,250 USD
Sell EUR or “hit the bid” : Sell $1M EUR and buy $1,348,200 USD
Base currency EUR, and quoted currency is USD
FX Classic Models
- Purchasing Power Parity (PPP) – “The Law of One Price” – In long run equilibrium exchange rates should converge to price ratios of identical baskets of goods assuming efficient markets and similar agents’ preferences, creation costs, frictionless markets, etc. Ex. Economist PPP “Big Mac” Index http://www.economist.com/content/big-mac-index
- Covered and Uncovered Interest Rate Parity (F forward rate, S spot rate)
- Covered (Pure Arbitrage) —- \((1+R_{(USD)}) = [F/S]*(1+R_{(FC)})\)
- Uncovered (Expected Arbitrage) —- \((1+R_{(USD)}) = [E(Š)/S]*(1+R_{(FC)})\)
- F: Forward Rate; S: Spot Rate; E(Š): Expected Future Spot Rate
- What factors drive FX?
- Interest rate differentials – e.x. “Carry-Trade”
- Real economy strengths/weaknesses
- Expected Inflation
- News that affects above
- Monetary policy/Flow of funds
Always remember the easy decomposition:
\[(R_{(USD)} – R_{(FC)} ) = (I_{(USD)} + r_{(USD)} ) – (I_{(FC)} + r_{(FC)} ) =\]
\[(I_{(USD)} – I_{(FC)} ) + (r_{(USD)} - r_{(FC)} )\]
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FX Carry : “Sort currencies into highest to lowest yielding currencies, buy the top and sell the bottom (Yen).”
G10 FX Carry
So, create an ETF/ETN out of it…
DBV – Deutsche Bank’s G10 Harvest Fund Carry ETF
ICI – Barclays Intelligent Carry Index (G10 currencies)
FX Carry vs Equity-Factors
Active FX Managers Examined
* First,
Let’s examine and index of actively managed currency hedge funds:
Barclay Currency Trader Index (BCTI)
Theoretical Motivation
Assume an APT multifactor model: \[R_{t} = \alpha + \Sigma_{i}\beta_{i}F_{i,t}+\epsilon_{t}\]
FX Four Factors Identified
- Carry DB Harvest / Citibank Beta1
- Trend-following (32, 61, 117 days) moving average
- Value +/-20% over/under PPP
- Volatility EURUSD & JPYUSD / 3-mon. Imp. Vol. 9 fx pairs (CVIX)
Factor 1: Carry
“Carry factor. We used the Deutsche Bank Currency Harvest G10 Index as the proxy for the returns of a carry strategy. This index reflects the return of being long the three high-yielding currencies against being short the three low-yielding currencies among the G–10 currencies. The index is rebalanced quarterly. Every quarter, the currencies are re-ranked according to their current three month LIBOR. The Bloomberg code for this factor is DBHVG10U.”
Factor 2: Trend
“Trend factor. We used the AFX Currency Management Index as a proxy for the trendfollowing factor.17 The AFX Index is based on trading in seven currency pairs weighted by their volume of turnover in the spot market, with returns for each pair based on an equally weighted portfolio of three moving average rules (32, 61, and 117 days).”
Factor 3: Value
“Value factor. We used the Deutsche Bank G10 Valuation Index as the proxy for the returns of a value strategy. To gauge relative value, Deutsche Bank prepares a ranking based on the average daily spot rate over the last three months divided by the purchasing power parity (PPP) exchange rate as published annually by the Organisation for Economic Co-Operation and Development. The Deutsche Bank G10 Valuation Index reflects the return of being long the three currencies with the highest rank (undervalued currencies) against being short the three currencies with the lowest rank (overvalued currencies) among the G–10 currencies. The Bloomberg code for this factor is DBPPPUSF.”
Factor 4: Volatility
“Currency volatility factor. We used the Deutsche Bank Currency Volatility Index as the proxy for foreign exchange volatility. This index is calculated as the weighted average of three-month implied volatility for nine major currency pairs (as provided by the British Bankers’ Association), with weights based on trading volume in surveys by the Bank for International Settlements. The Bloomberg code for this factor is CVIX. We used the first difference for this factor in Equation 1 because it is not a trading strategy. For the previous three factors, we used returns.”
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Next,
Let’s examine if individual currency managers’ crowd trades
How many FX managers?
How to measure if a trade is crowded?
Carry
Trend
Value
Hedge Funds Hegde?
“Do Hedge Funds Hedge?” by Asness et al
- Yes, hedge funds can provide significant diversification for traditional portfolios
- Examine, empirically, hedge fund indices CSFB/Tremont 1994-2000 (monthly data)
Simple regression shows modest market exposure and positive value added
But, this is very misleading…
- Since some HFs have illiquid securities and difficult to price OTC securities
- Positive serial correlation exists due to “stale” or “managed” prices
Once lagged betas are employed, find that hedge funds do not add value over this period
Stale or Manipulated Asset Prices?
- Weisman (2000) argues that hedge funds manage their reported monthly returns – “marketing supportive accounting”
- Stale prices can lower estimates of volatility and correlation to traditional indices
- Likely, Scholes and Williams (1977) and Dimson(1979) have techniques to account for illiquid securities
- Show that employing monthly returns to estimate betas and correlations understate market exposure
- Note study only hedge fund indices not individual hedge funds
Survivorship, Backfill, and Self-selection
- Data CSFB/Tremont (now DJ CS HF indices, employed in HWK1)
Data bias – Survivorship, Backfill, and Self-selection
- Data CSFB/Tremont (now DJ CS HF indices, employed in HWK1)
Data bias – Survivorship, Backfill, and Self-selection
Monthly vs Quarterly
Notice that monthly versus quarterly estimates of annualized standard deviation differ.
Hedge Fund Volatility
Notice that monthly versus quarterly estimates of annualized standard deviation differ.
Some Investment Models to Generate Alpha from CAPM Extensions
Sharpe-Lintner’s CAPM:
\[R_{i,t} = \alpha_{i} + \beta_{i}R_{m,t} + \varepsilon_{i,t}\]
Fama-French’s 3 Factor Model:
\[R_{i,t} = \alpha_{i} + \beta_{i}R_{m,t} + s_{i}SMB_{t}+ h_{i}HML_{t} + \varepsilon_{i,t}\]
Carhart’s Model:
\[R_{i,t} = \alpha_{i} + \beta_{i}R_{m,t} + s_{i}SMB_{t}+ h_{i}HML_{t} + m_{i}WML_{t} + \varepsilon_{i,t}\]
Lagged Betas
Apply Scholes and Williams (1977) and Dimson (1979) simple techniques
\[R_{i,t} = \alpha_{i} + \beta_{0i}R_{m,t} + \beta_{1i}R_{m,t-1} + \beta_{2i}R_{m,t-2} + \beta_{3i}R_{m,t-3}+...+\varepsilon_{i,t}\]
Fama-French’s 3 Factor Model:
\[R_{i,t} = \alpha_{i} + \beta_{i}R_{m,t} + s_{i}SMB_{t}+ h_{i}HML_{t} + \varepsilon_{i,t}\]
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## Call:
## lm(formula = AAPLexret ~ Mkt.RF + SMB + HML, data = ffhold)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.0164 -0.8426 -0.0340 0.7748 5.0299
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## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.1908 0.1225 1.558 0.12190
## Mkt.RF 1.3617 0.1584 8.597 3.45e-14 ***
## SMB -0.8402 0.3082 -2.726 0.00735 **
## HML -1.9321 0.3091 -6.251 6.35e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.363 on 121 degrees of freedom
## Multiple R-squared: 0.4744, Adjusted R-squared: 0.4613
## F-statistic: 36.4 on 3 and 121 DF, p-value: < 2.2e-16
Carhart’s Model:
Sharpe-Lintner’s CAPM Rewritten for Execution
\[\alpha_{i} = R_{i,t} - \beta_{i}R_{m,t} - \varepsilon_{i,t}\]
- To go long \(\alpha_i\) buy asset i and sell \(\beta_i\) time the asset i position of the index short with a derivative - expected return is \(\alpha_i\)
- To go short \(\alpha_i\) sell asset i short and buy \(\beta_i\) times the asset i position of the index short with a derivative - expected return is \(-\alpha_i\)
- These are market neutral positions and can be excuted independtly for each asset
Fama-French’s 3 Factor Model Rewritten for Execution
\[\alpha_{i} = R_{i,t} - \beta_{i}R_{m,t} - s_{i}SMB_{t}- h_{i}HML_{t} -\varepsilon_{i,t}\]
- Can still take out market factor with long/short index position, but left with SMB and HML factors
- There are not futures/derivatives on SMB or HML
- Solution is portfolio construction:
- Select weight for asset allocation to asset i, \(\omega_i\), such that \(\sum\omega_i s_i=0\) and \(\sum\omega_i h_i=0\)
- This leave the portfolio neutral to SMB, HML, and, using future as last step, \(R_m\)
- This portfolio is expected to earn \(\sum\omega_i \alpha_i\)
- To optimize return, maximize \(\sum\omega_i \alpha_i\) subject to \(\sum\omega_i s_i=0\) and \(\sum\omega_i h_i=0\) and then hedge residual \(R_m\) with future
- This will be similar process for other multi factor models such as Carhart, Fama-French 5 factor
- Note we could look at individual securities above, but now we have to execute an ensemble to achieve market neutral \(\alpha\)
Last step for portfolio contruction
Optimise for Sharpe by minimizing \(sigma(P)\)
- Remember there is en \(epsilon_i\) for each security
- Find \(\sum\omega_i \alpha_i/\sum\omega_i\omega_j \rho_{i,j}\sigma_i\sigma_j\) such that \(\sum\omega_i s_i=0\) and \(\sum\omega_i h_i=0\)
- Similar for Sharpe Lintner, maximize Sharpe but w/o added contraints
Fama-French’s 3 Factor Model:
\[R_{i,t} = \alpha_{i} + \beta_{i}R_{m,t} + s_{i}SMB_{t}+ h_{i}HML_{t} + \varepsilon_{i,t}\]
##
## Call:
## lm(formula = AAPLexret ~ Mkt.RF + SMB + HML, data = ffhold)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.0164 -0.8426 -0.0340 0.7748 5.0299
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## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.1908 0.1225 1.558 0.12190
## Mkt.RF 1.3617 0.1584 8.597 3.45e-14 ***
## SMB -0.8402 0.3082 -2.726 0.00735 **
## HML -1.9321 0.3091 -6.251 6.35e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.363 on 121 degrees of freedom
## Multiple R-squared: 0.4744, Adjusted R-squared: 0.4613
## F-statistic: 36.4 on 3 and 121 DF, p-value: < 2.2e-16
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## Call:
## lm(formula = AAPLexret ~ Mkt.RF, data = ffhold)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.2657 -0.9862 -0.1751 0.7242 7.0587
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.2184 0.1418 1.540 0.126
## Mkt.RF 1.1091 0.1597 6.947 1.92e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.58 on 123 degrees of freedom
## Multiple R-squared: 0.2818, Adjusted R-squared: 0.2759
## F-statistic: 48.26 on 1 and 123 DF, p-value: 1.916e-10
Carhart’s Model:
\[R_{i,t} = \alpha_{i} + \beta_{i}R_{m,t} + s_{i}SMB_{t}+ h_{i}HML_{t} + m_{i}WML_{t} + \varepsilon_{i,t}\]
Lagged Betas
\[R_{i,t} = \alpha_{i} + \beta_{0i}R_{m,t} + \beta_{1i}R_{m,t-1} + \beta_{2i}R_{m,t-2} + \beta_{3i}R_{m,t-3}+...+\varepsilon_{i,t}\]
Contributions
- “Do Hedge Funds Hedge” helped our industry better appreciate the differences in the return streams generated by the different hedge fund strategies
- Forced investors to think about the underlying liquidity of the positions that these hedge fund managers would generally hold
- Gave some insight to why a combination of hedge fund index strategies provided diversification benefits
Examine SMB, HML, and the “Market” - from Fama-French’s 3-factor model
Boring Old Factors…
Cumulative Returns
Add: Simple Trend Model
New Results
New Cumulative Returns
Comparing EW vs EW* (+36%!)
The defining discretionary global macro trade was by George Soros in Sept. 16th, 1992, when he bet on the devaluation of the British Pound
