There are obvious relationships between the various securities of a given firm that impact our expectations of risk. For example, if fixed income investors expect a corporate bond of a company to default, there must be a related bankruptcy event that would negatively impact shareholders in that firm. In this presentation, Nick will describe how to use data from bond and option markets to improve risk estimation for equity portfolios, and how to use information from the equity markets to improve estimation of credit risk in fixed income securities. The goal of the process is to create holistic risk estimation where all expectations of risk are mutually consistent across the entire capital structure of a firm, and related derivatives.

1. Using Cross-Asset Class
Information To Improve Portfolio
Risk Estimation
Nick Wade
Factset Risk Tour
March 2012

2. 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
www.northinfo.com

3. 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
www.northinfo.com

4. 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
www.northinfo.com

5. 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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6. 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
www.northinfo.com

7. 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)
www.northinfo.com

8. 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!
www.northinfo.com

9. 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
www.northinfo.com

10. 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
www.northinfo.com

11. 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.
www.northinfo.com

12. 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.
www.northinfo.com

13. 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:
Implied
Life:
Median
Cap-­‐ Revenue-­‐
Weighted
Weighted
Financial
22.28
17.06
7.86
Non-­‐Financial
14.74
18.42
17.60
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
www.northinfo.com

14. 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
Median
Average
Standard
Implied
Life
Implied
Life
Devia?on
July
31st
1995
DSI
400
17
17.91
9.93
S&P
500
14
15.40
9.28
March
31st
DSI
400
30
26.39
11.45
2010
S&P
500
30
24.93
10.92
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!
www.northinfo.com

15. “Sustainability” Equity Investing vs. MinVar
Mean
Annual
Monthly
CumulaGve
Monthly
Compound
Standard
Return
Return
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
www.northinfo.com

16. 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
www.northinfo.com

17. 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
www.northinfo.com

18. 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)
www.northinfo.com

19. 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
www.northinfo.com

20. Z-score Within Rating (January 2006 Through June 2011)
14 Cumulative Q1/Q5 Return Spread 1200
bps
up!
Doing
OK…
12
10
Peak
Value
November
8 2008
6
4
2
0
-2
Giving
it
all
back…
-4
www.northinfo.com
20

21. 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
www.northinfo.com

22. 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
www.northinfo.com

23. 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
www.northinfo.com

24. Conclusions
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
www.northinfo.com