Post on 18-Dec-2014
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Using Cross-Asset Class Information To Improve Portfolio Risk Estimation
Nick Wade Factset Risk Tour March 2012
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Northfield Risk for over 6 million traded securities globally, daily Over 300 client firms use our portfolio analytics to run anything from microcap
resources portfolios to enterprise risk The difficult stuff: unlisted assets; direct property and infrastructure, REITs, tax
sensitive rebalancing on over one million individual accounts We pioneered the adaptive hybrid model – learns as the market changes We launched the first production risk model to harness implied volatility – over 15
years ago From where we stand we are in a unique position to form a cohesive view of risk
and interactions across all marketable securities issued by a particular entity, and their interactions with other securities
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The Idea in Brief Any event or perception that has an effect on the size or uncertainty of the
future cashflows of an entity should affect the valuation and risk estimates of every marketable security issued by that entity, and every derivative security based upon them.
In stark contrast, a “traditional” risk model focuses in myopic fashion just on the
historical returns of a particular asset class. Our contention is that significant value can be added to the efficacy of risk
forecasts by exploiting the connections across asset classes, and harnessing a wide variety of “alternative” factors or conditioning information to arrive at expectations of risk that are mutually consistent across the entire capital structure of the firm, and related derivatives .
Harnessing Cross-Asset Class Information Makes Better Risk Forecasts
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Evidence of Linkage Market participants amplify connections across asset classes with “want to” and “have to”
trades. Diversification is weaker / absent in times of need. Khandani & Lo (2008) – quant meltdown of 2007 as asset class contagion vs. 1998 Russian
debt default Kritzman & Li (2010) – turbulence, contagion, skulls. During periods of market turmoil,
connections are much tighter. E.g. Normal -0.17, turbulent +0.76 Kritzman (again)… (2011) Systemic Risk: Absorption Ratio Connection for profit: - Capital structure arbitrage - Convertible bond arbitrage You need to have a good sense of the connections across asset classes in your risk model so that you can position your portfolio appropriately in any environment
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Really Obvious Cross-Asset Example “Traditional” Equity Risk Model Factors: Fundamental model: by construction looks to explore security risk just as a function of company
characteristics or attributes. A bit introspective… Macro models: in comparison look at other asset classes for signals:
Oil prices – commodity asset class affects equity asset class How? Energy cost to companies.
Interest Rates – fixed income asset class affects equity asset class How? Financing cost.
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Example: Harnessing New Signals 1997 Northfield Short Term Model (Nick Wade, Bob Kelley) Information from the option market conditions risk forecasts of the underlying
individual securities and their shared (factor) behavior; model balances historical behavior with market consensus forecast behavior over the term of the option contract.
2007 Northfield Near-Horizon Models (Anish Shah) A variety of signals can be used to condition risk forecasts… implied volatility, cross-
sectional dispersion, volume, open interest 2009 diBartolomeo, Mitra, Mitra – Using Quantified News Flows Non-traditional contemporaneous or forward-looking signals enhance model
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Bit More Complicated… Structural Models Merton (1974): an equity security can be considered a call option on the assets
of the firm. Alternatively, the lenders are short a put. Various nuances: - Black and Cox (1976) “first passage” - Bookstaber and Jacob (1986) “composite hedge” - Leland (1994), Leland & Toft (1996) “tax issues”…and on and on… Simple way to think of it: A corporate bond can be represented as a government bond plus an
equity position. Corporate bond risk can be represented as government bond risk plus
equity risk (credit risk)
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Credit Risk We derive a solution of corporate bond’s credit factor exposures which are directly
related to the factor exposures of the associated company’s stock. The relation has the form: Factor Exposure Bond = -(E/B) * (delta put/delta call) * Factor Exposure Of the Stock
of the Bond Issuer Where; E is the market capitalization of the firm B is the market value of the firm’s debt …and the put and call are calculated with respect to the maturity of the particular
bond tranche With a model of 70,000 listed equities, we are in good shape to model credit
even for illiquid bonds!
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Why is this better? You could use ratings, but (in case you’ve been on Mars for the last three years) to
be honest they aren’t well regarded currently… You could use a history of actual defaults and several hundred fundamental analysts
and try and make better ratings… You could use spread changes (and we did) but estimating a decent spread requires
first of all having a decent price. And given the liquidity issues with corporate debt (and even government debt “off the run”) the prices are noisy.
Leveraging the connection with equities allows us to: Harness the most liquid market information (equities and options) Harness forward-looking signals e.g. implied volatility / implied correlation This allows us to adjust credit risk to reflect a change even if the bond didn’t
trade or the market is closed
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Implications Factor Exposure Bond = -(E/B) * (delta put/delta call) * Factor Exposure Of the
Stock of the Bond Issuer 1. The closer the firm is to default (deeper into junk status) the higher the delta
of the put will be relative to the delta of the call. Given that option gamma is the same for puts as for calls the approach to junk status will tend to proportionately increase the ratio of two deltas more than it will decrease the ratio E/B per unit of decline in the firm asset value. That will make the bond’s factor exposures more similar to that of the stock and this reflects the empirical evidence that junk bonds w behave like equities.
The closer the firm is to default, the more similar the bond’s factor
exposures become to those of the stock - reflecting the empirical evidence that junk bonds behave like equities
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Implications 2 Factor Exposure Bond = -(E/B) * (delta put/delta call) * Factor Exposure Of the Stock of the
Bond Issuer Short term bonds of the same company are more volatile than the longer term bonds of
the same firm (just talking about credit risk here!) With shorter-dated options the put deltas are higher and the call deltas lower than those of
longer-dated options And this of course reflects the conventional logic that the longer term provides more room than
short term towards unbounded improvement than bounded decline. Despite that simple logic, the anecdotal bias in the industry has is that longer term bonds are
more credit risky than shorter term ones, partly due to bond duration vis-à-vis spread considerations, and confusion of higher periodic volatility with higher total premium charged for default risk (firm put option value).
Our finding sets the record straight and is one of the contributions of the model to a better
accord of mathematical rigor and conventional intuition in the area of finance.
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Market Implied Expected Life Using a structural model and our estimates of equity volatility estimate
the “market implied expected life” of firms • For a 50% probability of default threshold, work the option math backwards to give us
the implied expiration of the option, which we term the “implied life” of the firm. • See Yaksick (1998) for numerical methods for evaluating a perpetual
American option (include term-structure of interest rates) • Makes different default probabilities for different bond issues very natural as
each maturity will lie at a different point in the survival time distribution
See diBartolomeo, Journal of Investing December 2010 A quantitative measure of the fundamental and “social” concept of sustainability The “sustainability” aspect of the credit risk stuff is also a way for
quants and fundamental investors to talk in a common language. To long-term fundamental investors, “risk” is the potential for a company to fall apart and go bankrupt. We now explicitly measure that.
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Previously Published Research Estimate market implied life monthly for all firms in Northfield US equity universe
December 31st 1991 to March 31st 2010. Mix of large and small firms, 4660 – 8309 names
Contrast two sub-samples: Financial Firms, Non-financial firms:
Risk taking is heavily concentrated in the largest financial firms Risk taking has been concentrated in the largest financial firms for at least 20 years
Implied Life: Median Cap-‐Weighted
Revenue-‐Weighted
Financial 22.28 17.06 7.86
Non-‐Financial 14.74 18.42 17.60
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Quantifying “Sustainability” MSCI KLD DSI 400 index of US large cap firms considered
socially responsible, 20 year history • Typically about 200 firms in common with the S&P 500 • Statistically significant difference in means
Testing on disjoint sets (i.e. DSI not S&P, S&P not DSI) Statistically significant difference in means for every time period
tested – socially responsible firms are expected to live longer!
Median Implied Life
Average Implied Life
Standard Devia?on
July 31st 1995 DSI 400 17 17.91 9.93
S&P 500 14 15.40 9.28
March 31st 2010
DSI 400 30 26.39 11.45
S&P 500 30 24.93 10.92
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“Sustainability” Equity Investing vs. MinVar Mean Annual
Monthly CumulaGve Monthly Compound
Return Return Standard DeviaGon Return
Q5 Equal 1.33 713.77 9.15 10.90
Q1 Equal 1.03 790.86 3.64 11.50
Q5 Cap 0.77 251.60 6.62 4.98
Q1 Cap 0.79 414.32 3.78 7.77
S&P 5002 0.75 347.74 4.32 6.78
Q5 MV 1.77 2901.15 6.80 19.33
Q1 MV 1.07 840.43 2.96 12.34
(QuinGles by Implied Life, 1992 through March 2010, maximum of 200 posiGons) MinVar construc<on benefits only apparent in “junk” quin<le
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The Value Premium When we invest in financially troubled “value” firms
• These firms have obvious have bankruptcy potential • We value these firms knowing they can go broke
When we invest in healthy “growth” firms
• We assume they will exist in perpetuity • In a DDM context most of the cash flows to be discounted tp
present value occur further in the future • If growth firms have finite lives those far in the future cash flows
never happen and DDM will systematically overvalue these firms • Anybody remember Digital Equipment?
The sustainability framework provides a potential explanation for the widely observed “value” return premium
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Forecasting rating changes and making money As part of our normal fixed income analysis we estimate “option-adjusted spreads”
for about 6 Million fixed income instruments on a monthly basis We combined rating levels from S&P, Moody’s and Fitch into a unified letter scheme
and then quantified them “AAA” at 10, “D” at 1, and scale intermediate levels inversely proportional to OAS
Predict rating change: the percentage change in the “simple” numerical value of the credit rating
…using implied life variables:
• 12 month percentage change in expected life as of prior month end • 12 month change in the cross-sectional Z-score of expected life
within the US equity universe
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A Modest But Encouraging Result Even with our simple model we could meaningfully predict
subsequent changes in bond ratings
• Our model had a correlation of about 40%, R-squared of 0.16 • A very high degree of statistical significance on coefficients (T > 4) • R-squared was higher for subsets of lower grade bonds (i.e. NOT
“A”) • These results are all conditional that a change in rating would
eventually take place since only such events existed in our data • Non-events (no rating change) were excluded from the sample by
design
Perhaps our model would predict 14 of every 5 downgrades (Data: 8500 events from Barrons, 1992 – 2008)
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Comparison with Credit Rating Agencies Create a metric to compare our ratings to the published ratings: At each year end starting at 2005 we convert the expected life of issuer for each bond issue to
a Z score within rating category A negative Z score indicates that our metric suggests that the firm is less creditworthy than the
published rating Sort sample universe of 22000 bond issues into quintiles by Z score for 12/31/2006 (and nearly
identical result for 12/31/2007): Bottom quintile of 4400 bond issues: 2940 were from Wall Street firms that either went
bankrupt, were acquired or needed major government assistance The rogues gallery included:
• Bear Stearns (534 issues), Merrill Lynch (868), Lehman Brothers (657), Morgan Stanley (257), CIT Financial (338), Countrywide (136) and Washington Mutual (24)
The model correctly identifies the biggest credit risks during GFC
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Z-score Within Rating (January 2006 Through June 2011)
-4
-2
0
2
4
6
8
10
12
14 Cumulative Q1/Q5 Return Spread
20
Peak Value November 2008
1200 bps up!Doing OK…
Giving it all back…
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Default Correlations – our goal is joint probabilities
No model of credit risk is complete without the ability to estimate default correlations
Defaults are usually rare events so it’s impossible directly to observe default correlations over time
However, Equity return volatility and correlation are readily observable Zeng and Zhang (2002) shows asset correlations must arise from correlation of
both equity and debt components Qi, Xie, Liu and Wu (2008) provide complex analytical derivation of asset
correlations given just equity return correlation Interim result - we end up with asset correlations and asset volatilities
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Joint Default Probabilities
With asset volatility and correlations estimated we can use our preferred structural model to estimate default probability of a firm
Use method from Zhou (2001) to convert asset correlations to default correlations
We can now produce joint default probabilities across firms
However there are some pretty restrictive assumptions • Firm must have debt today • Firm must have positive book value today • Balance sheet leverage must stay fixed in the future
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Another Angle on Default CorrelaGons For example, if an event that causes a large change in the expected life of Bond X also causes a similarly large change in the expected life of Bond Y then their fates are likely intertwined. Formalize: Once the time series of expected lives have been calculated: we can estimate default correlation as the correlation of percentage changes in expected lives across firms Better than trying to correlate OAS spreads since bond prices are driven by liquidity effects
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Risk Models that exploit the connections across asset classes can greatly improve our ability to forecast risk and position portfolios safely in all environments
From our vantage point across all asset classes – whether listed or unlisted – we are in an excellent position
to create a holistic and mutually consistent representation of the risk of all marketable securities and derivatives issued by a particular firm; each individual part enhanced by its linkage to the rest.
Our model for credit risk harnesses our research and signals from equity risk, together with other non-
traditional signals. Our model for the expected life of firms effectively combines equity factor risk models and contingent claims
credit models in a unified framework Using expected life data as a metric for corporate credit risk allows for effective prediction of credit rating
changes, an explanation for the “value” premium, quantifies the fundamental qualitative concept of “sustainability”, and generates substantial alpha from corporate bond portfolios by using expected life related metrics as a better measure of credit risk
Minimum variance portfolio construction is helpful, but has more impact when used in conjunction with
sustainability
Conclusions