New Practice Questions
1. Risk-neutral pricing: @Jaskarn asked a good question about the credit value adjustment (CVA) that touches on a theme in derivatives: https://trtl.bz/2ULV72V The question is about Jon Gregory's statement that CVA is compatible with either the financial product's actuarial price or the risk-neutral price. This is thematic because risk-neutral pricing is a topic in John Hull's derivative assignment and in Tuckman's review of interest rate term structure models. If that's not enough, it also appears in Malz's discussion of default intensity models. Part 2 candidates do want to understand, for example, the difference between risk-neutral and real-world default probabilities.
2. BSM assumptions: @RYS asked about the Black-Scholes Merton option pricing model (BSM OPM) assumptions https://trtl.bz/2ULVKtj This might seem academic but the BSM shows up in a lot of places and its assumptions have been borrowed into unexpected places. For example, many public companies use BSM to estimate their employee stock option (ESO), although an FRM candidate might understand the arguments in favor of the binomial model for such a purpose. Many analysts use BSM to value real options. In my previous life, I consulted to Boards on valuation so I have some experience defending these models. It's really important to understand the assumptions of the BSM, because they are very restrictive. Actually, they are unrealistic. But I don't think that renders the BSM useless. All models, to some degree, are unrealistic. Models simplify. Also, the BSM models assume the lognormal property of the asset price, a so-called diffusion process in continuous time. This might be the most common assumption about stock price dynamics, if only because it's the first one taught. But it is hardly (not even close) the only model for stock prices.
3. Foreign exchange (FX) quote convention: @JanaRad asked for help identifying the arbitrage trade when a foreign exchange (FX) futures contract is mis-priced https://trtl.bz/2UQzC0E. I don't think this is easy for anybody, except maybe currency professionals. Along the way, we've provided some input to GARP: we helped establish the consistent use of FX currency quote conventions. In this vein, you will see authors refer to the foreign-versus-domestic currency. However, my recommendation is to ignore that in favor of the base-versus-quote distinction, which follows the market convention. In the currency priority rankings, for example, the Euro ranks above the dollar; therefore, proper is EURUSD $1.126 where EUR is the base and USD is the quote. In the cost of carry model (and its interest rate parity variation), then, the EUR is the commodity, like cotton or copper or the S&P 500 Index is a commodity. And the USD is the price of the commodity. For me the key to mastery here includes these two items: (i) clarity on the FX quote convention and (ii) treating the base currency as if it were the commodity. Then I think the logic of the arbitrage follows naturally.
4. Quantile-quantile (QQ) plot: Every year there are questions about the QQ plot; e.g., https://trtl.bz/2UQzC0E. Its inclusion in the FRM is completely understandable: quantitative risk is a lot about the specification (and estimation) of a future distribution. I don’t mean to over-simplify, but isn't that the hard work? If we can successfully specify a future distribution, we've overcome the problem of Knightian uncertainty https://en.wikipedia.org/wiki/Knightian_uncertainty and many business needs become utterly solvable; e.g., risk capital attribution. But it's audacious to pretend to be able to anticipate the future. In practice, the exercise often amounts to the comparison of a lumpy, messy historical (aka, empirical) distribution to a clean parametric function. Enter the utility of the QQ plot! However, I confess that I find them hard to interpret myself. Only by talking with candidates on the forum did I start to grok them a bit. If you are new to QQ, here is my recommendation: study them sufficiently so that you know which features betray positive/negative skew and heavy/light tails in comparison to the normal distribution. For example, what graphical feature betrays left (aka, negative) skew; can you quickly identify negative skew?
External
1. A random forest is many decision trees. One of the best assigned readings in Current Issues (Part 2 Topic 9) is Hal Varian's Big Data: New Tricks for Econometrics (https://trtl.bz/2VhNq3H). It contains a nice introduction to decision trees using the famous Titanic dataset. In January I spent a week at a data science bootcamp where we participated in a contest using the Titanic dataset, it's a popular training set. My best source for good articles is Medium. For example, this week was published The Complete Guide to Decision Trees https://trtl.bz/2GvFGSB. Also, Random Forests for Complete Beginners https://trtl.bz/2GtyVR1 (If you want a GENTLER introduction: Decision Trees--An Intuitive Introduction https://trtl.bz/2CQ7Bui; for something more dense, here is a good tutorial from Analytics Vidhya https://trtl.bz/2GqwajA).
2. The hard problem of helping people reskill without taking forever. I started Bionic Turtle because I wanted more than anything else to be in the business of helping people add skills to get better jobs. It's a very different perspective than thinking of yourself as a publisher of learning materials. Publishing content is easier than helping customers develop skills. So I was very interested in this: Why Companies Are Failing at Reskilling (In a tight labor market, employers from Amazon to JPMorgan are trying to get better at retraining the workers they have) https://trtl.bz/2GyhsH4 When I started BT many years ago, I attended several eLearning conferences (I even presented at one where I shared my object-oriented software kit, which did not take off with customers). Even when I was new to the field, I could tell that too many approaches were simply too slow: the people and time and cost of a traditional instructional design can be rather weighty and lumpy, for lack of a better word. That's even more true today. Speed is absolutely essential. If you can't be fast, you can't make a work. As the article says, "Employers are still trying to master the challenge of mapping the skills of their current workers, identifying the skills required of their future workforce and filling the gaps between the two. By the time many companies figure out exactly who they need, it’s often too late to invest the necessary time and money into retraining."
3. Cryptocurrency risks: I will confess (or is It a boast?) that I hold some cryptocurrencies; I think it's okay to allocate a very small percentage of your portfolio to highly speculative investments. I sold most of my bitcoin subsequent to its peak (at a price of $10,636 per coin, so my timing was neither terrific nor terrible). My issue with this asset class is that I personally do not know how to analyze cryptocurrencies as fundamental investments: if the only thing I do is watch price and volume, then I am just being a technician, or worse, just a timer. They seem to trade on sentiment and profile. Probably I just don't know enough about the sector. In any case, here is an informative summary of regulator perspectives on crypto by John Hintze at the GARP site: The BIS-BCBS-FSB View of Crypto (Risk guidance takes shape from a series of the global oversight bodies’ pronouncements) https://trtl.bz/2UPowcs.
- P1.T4.915. Country risk measures and historical instances of sovereign default (Damodaran) https://trtl.bz/2UO5nYf
- P2.T6.906. Features of a collateralization agreement (Gregory Ch.6) https://trtl.bz/2UQHy23
- Fixed Income: Infer discount factors, spot, forwards and par rates from swap rate curve (FRM T4-25) https://trtl.bz/2vfGBRO
- Fixed Income: Maturity versus Bond Price (FRM T4-26) https://trtl.bz/2XCalod
1. Risk-neutral pricing: @Jaskarn asked a good question about the credit value adjustment (CVA) that touches on a theme in derivatives: https://trtl.bz/2ULV72V The question is about Jon Gregory's statement that CVA is compatible with either the financial product's actuarial price or the risk-neutral price. This is thematic because risk-neutral pricing is a topic in John Hull's derivative assignment and in Tuckman's review of interest rate term structure models. If that's not enough, it also appears in Malz's discussion of default intensity models. Part 2 candidates do want to understand, for example, the difference between risk-neutral and real-world default probabilities.
2. BSM assumptions: @RYS asked about the Black-Scholes Merton option pricing model (BSM OPM) assumptions https://trtl.bz/2ULVKtj This might seem academic but the BSM shows up in a lot of places and its assumptions have been borrowed into unexpected places. For example, many public companies use BSM to estimate their employee stock option (ESO), although an FRM candidate might understand the arguments in favor of the binomial model for such a purpose. Many analysts use BSM to value real options. In my previous life, I consulted to Boards on valuation so I have some experience defending these models. It's really important to understand the assumptions of the BSM, because they are very restrictive. Actually, they are unrealistic. But I don't think that renders the BSM useless. All models, to some degree, are unrealistic. Models simplify. Also, the BSM models assume the lognormal property of the asset price, a so-called diffusion process in continuous time. This might be the most common assumption about stock price dynamics, if only because it's the first one taught. But it is hardly (not even close) the only model for stock prices.
3. Foreign exchange (FX) quote convention: @JanaRad asked for help identifying the arbitrage trade when a foreign exchange (FX) futures contract is mis-priced https://trtl.bz/2UQzC0E. I don't think this is easy for anybody, except maybe currency professionals. Along the way, we've provided some input to GARP: we helped establish the consistent use of FX currency quote conventions. In this vein, you will see authors refer to the foreign-versus-domestic currency. However, my recommendation is to ignore that in favor of the base-versus-quote distinction, which follows the market convention. In the currency priority rankings, for example, the Euro ranks above the dollar; therefore, proper is EURUSD $1.126 where EUR is the base and USD is the quote. In the cost of carry model (and its interest rate parity variation), then, the EUR is the commodity, like cotton or copper or the S&P 500 Index is a commodity. And the USD is the price of the commodity. For me the key to mastery here includes these two items: (i) clarity on the FX quote convention and (ii) treating the base currency as if it were the commodity. Then I think the logic of the arbitrage follows naturally.
4. Quantile-quantile (QQ) plot: Every year there are questions about the QQ plot; e.g., https://trtl.bz/2UQzC0E. Its inclusion in the FRM is completely understandable: quantitative risk is a lot about the specification (and estimation) of a future distribution. I don’t mean to over-simplify, but isn't that the hard work? If we can successfully specify a future distribution, we've overcome the problem of Knightian uncertainty https://en.wikipedia.org/wiki/Knightian_uncertainty and many business needs become utterly solvable; e.g., risk capital attribution. But it's audacious to pretend to be able to anticipate the future. In practice, the exercise often amounts to the comparison of a lumpy, messy historical (aka, empirical) distribution to a clean parametric function. Enter the utility of the QQ plot! However, I confess that I find them hard to interpret myself. Only by talking with candidates on the forum did I start to grok them a bit. If you are new to QQ, here is my recommendation: study them sufficiently so that you know which features betray positive/negative skew and heavy/light tails in comparison to the normal distribution. For example, what graphical feature betrays left (aka, negative) skew; can you quickly identify negative skew?
External
1. A random forest is many decision trees. One of the best assigned readings in Current Issues (Part 2 Topic 9) is Hal Varian's Big Data: New Tricks for Econometrics (https://trtl.bz/2VhNq3H). It contains a nice introduction to decision trees using the famous Titanic dataset. In January I spent a week at a data science bootcamp where we participated in a contest using the Titanic dataset, it's a popular training set. My best source for good articles is Medium. For example, this week was published The Complete Guide to Decision Trees https://trtl.bz/2GvFGSB. Also, Random Forests for Complete Beginners https://trtl.bz/2GtyVR1 (If you want a GENTLER introduction: Decision Trees--An Intuitive Introduction https://trtl.bz/2CQ7Bui; for something more dense, here is a good tutorial from Analytics Vidhya https://trtl.bz/2GqwajA).
2. The hard problem of helping people reskill without taking forever. I started Bionic Turtle because I wanted more than anything else to be in the business of helping people add skills to get better jobs. It's a very different perspective than thinking of yourself as a publisher of learning materials. Publishing content is easier than helping customers develop skills. So I was very interested in this: Why Companies Are Failing at Reskilling (In a tight labor market, employers from Amazon to JPMorgan are trying to get better at retraining the workers they have) https://trtl.bz/2GyhsH4 When I started BT many years ago, I attended several eLearning conferences (I even presented at one where I shared my object-oriented software kit, which did not take off with customers). Even when I was new to the field, I could tell that too many approaches were simply too slow: the people and time and cost of a traditional instructional design can be rather weighty and lumpy, for lack of a better word. That's even more true today. Speed is absolutely essential. If you can't be fast, you can't make a work. As the article says, "Employers are still trying to master the challenge of mapping the skills of their current workers, identifying the skills required of their future workforce and filling the gaps between the two. By the time many companies figure out exactly who they need, it’s often too late to invest the necessary time and money into retraining."
3. Cryptocurrency risks: I will confess (or is It a boast?) that I hold some cryptocurrencies; I think it's okay to allocate a very small percentage of your portfolio to highly speculative investments. I sold most of my bitcoin subsequent to its peak (at a price of $10,636 per coin, so my timing was neither terrific nor terrible). My issue with this asset class is that I personally do not know how to analyze cryptocurrencies as fundamental investments: if the only thing I do is watch price and volume, then I am just being a technician, or worse, just a timer. They seem to trade on sentiment and profile. Probably I just don't know enough about the sector. In any case, here is an informative summary of regulator perspectives on crypto by John Hintze at the GARP site: The BIS-BCBS-FSB View of Crypto (Risk guidance takes shape from a series of the global oversight bodies’ pronouncements) https://trtl.bz/2UPowcs.
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