Blog Week in Risk (ending March 26th)

David Harper CFA FRM

David Harper CFA FRM

David Harper CFA FRM
Subscriber
New practice questions
In the forum this week (selected only) or Major News
Political and regulatory risk, including Systemic Risk (including BIS)
Technology, including FinTech and Cybersecurity
Natural Science, including Climate and Energy
Data science (primarily R), including Alternative Data
Personal finance
Other
Enterprise risk management (ERM) including governance
Case Studies and Companies, including Strategic or Reputation risk
Risk Foundations (FRM P1.T1)
Quantitative Analysis (FRM P1.T2)
Financial Markets and Products, including Interest Rates, Commodity Risk, and Foreign Exchange (FX)(FRM P1.T3)
  • Rookie Currency Traders Are Causing Big Problems https://www.bloomberg.com/news/arti...raders-are-causing-trouble-at-crucial-moments “Tucked deep into a report on foreign-exchange market liquidity was a brief paragraph on how rookie traders could be partly to blame -- along with falling volumes and the growing prevalence of electronic trading -- for the flash crashes that have roiled the $5.1-trillion-a-day currency market over the past two years.”
  • Covered Interest Parity http://johnhcochrane.blogspot.com/2017/03/covered-interest-parity.html “The covered interest rate parity relationship fell apart in the financial crisis. And that's understandable. To take advantage of it, you first have to ... borrow dollars. Good luck with that in fall 2008. Long-only investors had more important things on their minds than some cockamaime scheme to invest abroad and use forward markets to gain a half percent per year or so on their abundant (ha!) cash balances. The amazing thing is, the arbitrage spread has not really closed down since the crisis.”
  • What makes gambling wrong but insurance right? http://www.bbc.com/news/business-38905963 “The ability to buy derivatives lets companies specialise in a particular market. Otherwise, they would have to diversify - like the Chinese merchants four millennia ago, who didn't want all their goods in one ship. The more an economy specialises, the more it tends to produce. But unlike regular insurance, for derivatives you don't need to find someone with a risk they need to protect themselves against. You just need to find someone willing to take a gamble on any uncertain event anywhere in the world.” [it’s called an insurable interest]
  • Why It Matters How We Define Insurance (Some types of insurance charge people according to risk. Others don't. On health care, Americans are caught between the two) http://blogs.wsj.com/economics/2017/03/24/why-it-matters-how-we-define-insurance/ Smart take: "It depends on what you mean by insurance. The basic idea is that a community pools its resources to compensate individuals who suffer some peril such as sickness, death or fire. Pure insurance covers only random perils. Predictable perils generally require higher premiums ... Over time, though, society has increasingly blended subsidies with insurance. Social Security, for example, effectively requires younger, affluent, able-bodied workers and two-earner couples to subsidize older, less affluent and disabled workers and one-earner couples."
  • What if breakeven inflation and the “term premium” are measuring the same thing? https://ftalphaville.ft.com/2017/03...he-term-premium-are-measuring-the-same-thing/
  • 0% Financing Deals Bite Back Retailers as Fed Raises Rates (Companies will likely absorb the extra cost on no-interest purchases, hoping rate boost is a sign of an improving economy) https://www.wsj.com/articles/fed-ra...ng-deals-more-pricey-for-retailers-1490261405
Valuation and Risk Models, including Country risk (FRM P1.T4)
  • A Valeant Update by Professor Aswath Damodaran http://trtl.bz/2mKUmWF Really interesting introspection by one of my favorite value investors
  • The Art of (Illiquid) Securities Pricing http://expectedloss.blogspot.in/2017/03/the-art-of-illiquid-securities-pricing.html "Since the crisis, the SEC has ramped up its investigations into pricing issues, and in 2013 set in motion three initiatives (the Financial Reporting and Audit Task Force; the Microcap Fraud Task Force; and the Center for Risk and Quantitative Analytics). There has been a steady and growing stream of findings of asset valuation mismanagement. Some hedge funds have been shut down. (A list of issues here.)"
Credit risk (FRM P1.T6)
Investment risk, including Alternative Investments and Pensions (FRM P1.T8)
Current issues (FRM P2.T9)
 
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David Harper CFA FRM

David Harper CFA FRM

David Harper CFA FRM
Subscriber
In case you are interested, based on the good question from @RobKing at https://forum.bionicturtle.com/threads/p2-t6-304-single-factor-credit-risk-model.6806/#post-48931, I just wrote the following text below for the next revision to the R44.P2.T6 Malz Study Note in order to slowly explain a perennially challenging LO (Malz Chapter 8: "Describe the use of a single factor model to measure portfolio credit risk ...).

This is meant to explain the exhibit that summarizes Malz' Example 8.4:

0401-malz-single-factor.png


"We start by assuming an unrealistic single-factor model where the firm’s asset return is given by a(i) = β(i)*m + sqrt[1-β^2(i)]*e(i). This model has a certain resemblance to the capital asset pricing model (CAPM) because the firm’s asset return is a combination of a systemic component, β(i)*m, and a firm-specific shock, sqrt[1-β^2(i)]*e(i). Beta, β(i), is the firm’s exposure to the shared common factor, given by (m), which represents the economic state. The random e(i) is important because it represents the random shock in the form of a random standard normal variable, N(0,1). But why is e(i) scaled by sqrt[1-β^2(i)]? This is by design of the overall model which is unrealistic but extremely convenient. If we make the four assumptions stated by Malz in Malz 8.3.1 (i.e., that both the common factor, m, idiosyncratic shock, e, are standard normals and that the idiosyncratic shocks are neither correlated with themselves nor m), then per summation stability, the asset return, a(i) will be a random standard normal variable, too! In this way, the elegance of this single-factor model is that it transforms a standard random normal shock, e(i), into a standard random normal variable that is influenced by the common factor, m, to the extent of the firm’s beta, β(i).

Assuming the model, we are given the two key assumptions that tell us about the firm: its beta and its unconditional default probability. As shown in the exhibit, Malz’ example 8.4 assumes beta, β(i) = 0.40 and an unconditional PD of 1.0%. From the unconditional PD, we can infer the normal quantile of -2.326 = NORM.S.INV(0.010). So this k = -2.326 is the firm’s default threshold. As Malz says about k = -2.33, "If we were in a stable economy with m = 0, we would need a shock of −2.33 standard deviations for the firm to die."

Having established the unconditional default threshold (i.e, k = - 2.33), the next step is the whole point of the model: to estimate a conditional default probability that is updated with specific information about the economic state as represented by the value of the common factor (m). Recall that (m) is a standard normal and m = 0 represents a “stable economy,” such that Malz represents a “modest economic downturn” with m = -1.0 and a “more severed economic downturn” with m = -2.33. Yes, it’s true, this is a highly (ridiculously?) abstract representation, but at the same time, setting m = -2.33 is a way of saying “this economic state only gets this bad about 1.0% of time.” The essence of this model is an extremely simple representation of an economic state and each firm's sensitivity to that economic state. Now we simply update the single-factor asset return model with the new information—i.e., m = -1.0 or m = -2.33—such that we’ve got, in the first case the following model for the firm’s asset return during a modest economic downturn: a(i) = β(i)*m + sqrt[1-β^2(i)]*e(i) = 0.40*(-1.0) + sqrt[1-0.40^2]*e(i). As e(i) is a random standard normal, I will now replace it with Z.

Finally, given that we have a conditional (that is, conditional on the economic downturn as reflected in the m = -1.0 input) model for the firm’s asset return of a(i) = 0.40*(-1.0) + sqrt[1-0.40^2]*Z, we can infer the conditional default probability by solving for the (Z) that returns an a(i) equal to the default threshold of -2.33. This is similar to the Merton model because, as shown below, the distance to default is given by DD = k(i) - β(i)*m; in the modest case, this distance to default is the distance from the asset’s conditional mean of β(i)*m = 0.40*-1.0 = -0.40 and the default threshold of -2.326, so the DD = -2.326 - (0.40*-1.0) = -1.926. After we standardize, by dividing by the conditional volatility, we get a Z = -2.102 (in the modest downturn) or Z = -1.51 (in the severe downturn). These (Z) variables are simply standardized distances to default: they tell us how many standardized standard deviations the idiosyncratic variable, e(i), must shock in order for the firm to default. In the modest economy, N(-2.102) = 1.78% and this is the conditional default probability. In the severe economy, which has the same default threshold of k = -2.33 but where the firm’s expected value is lower so that its distance to default is shorter, the conditional PD goes up to N(-1.521) = 6.41%.

To summarize (in the case of the modest downturn), the firm’s unconditional default probability is 1.0% because it defaults if random standard normal k ≤ -2.33. The single-factor model assumes the firm’s asset return is also a function of exposure, β(i), to the economic state, given by (m). An adverse economic state, represented by (m < 0), updates the firm’s expected return (and conditional volatility) so that the firm’s conditional default probability is given by the probability of breaching the same default threshold (i.e., k = - 2.33) but under the conditional distribution that is informed by the economic state. More abstractly, (m <> 0) translates the unconditional standard normal, where it is simply the case that PD = 1.0% = NORM.S.DIST(-2.33, true), into a conditional standard normal, a(i), and its conditional default probability given by Pr[a(i) ≤ k]."
 
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