# Tag Info

## Hot answers tagged risk

16

I can think of three reasons. First, and simplest, is that people care about variance. Second, if you really do care about draw-downs, if returns are close to normally distributed, the distribution of draw-downs is just a function of the variance, so there's no need to include draw-downs explicitly in your portfolio construction objective. Minimizing ...

15

I guess it depends on what they're referring to... The traditional swap curve (LIBOR-based) is certainly not risk free, as evidenced by the experience of the financial crisis and the resulting migration to OIS discounting. The OIS curve (which is a kind of swap curve...) is now the standard risk-free curve. The Treasury yield curve is not favored, because ...

12

E.g. on Monday you get forced to buy some Friday expiry OTM puts, say 95% strike S&P weeklies. Of course, you go and buy some delta against them to "hedge" yourself. Next thing you know, the the market tanks. Unfortunately, by Friday it's only down 3.5%, so it's does not fall far enough to reach the strike. So, on Friday expiration, you are out your ...

12

The majority of the movement in currencies is in the spot rates, rather than in the term structure. A 3-month rolling hedge would always be protecting against movements in the spot rates, no matter when they happen. Using your example, if the current EUR/USD rate is 1.3333, you might be able to get a 3-month forward at 1.3339. (Forgive me if I have the ...

10

The underlying problem: your ACTR constraints aren't convex The $i$th constraint on your risk contribution can be written: $$w_i \sum_j \sigma_{ij} w_j \leq c_i s$$ And this isn't a convex constraint because of the $w_j w_i$ terms (a function $g(x,y)=xy$ isn't convex in $x$ and $y$). They're not convex constraints, so you won't be able to write them as ...

9

A market is said to be complete if any contingent claim can be replicated by an admissible (i.e. with value process bounded from below) self-financing (i.e. all gains and losses exactly offset each other) trading strategy, a so-called replicating strategy. This strategy being constructed from primary securities - the market prices of which are unique - it ...

9

There is no definitive answer to this question and there are infinite papers out there. I personally think they are better explained as mispricings. Several points: 1) Persistence of HML does not imply it has to be a risk factor. If there are idiosyncratic mispricings in individual stocks, then by construction, the ones that look cheap are going to be ...

9

Values of VaR are just the inverses of the cumulative distributions. CVaR is not a very commonly used term, its more frequently used synonym is Expected Shortfall. See http://www.maths.manchester.ac.uk/~saralees/chap17.pdf for the list of Expected Shortfall values for more than 20 distributions.

9

A better, clearer, answer is to compute Lambda (leverage) of the option (link) and see if it is bigger or smaller than 1. Lambda is $\Delta \frac{S}{V}$ so we test $$\Delta \frac{S}{V} \lessgtr 1$$ which is what Joshi is saying in words: compare $\frac{1}{S}$ (delta to price for the stock, the delta of the stock is 1) to $\frac{\Delta}{V}$ (delta to price ...

7

If you have the mathematical sophistication, you should review the original papers referenced on the Equity Premium Puzzle page, particularly Mehra and Prescott (1985). Note, however, that contrary to other opinions on this page, the puzzle is NOT that there is an equity risk premium. On the contrary, the puzzle is that the premium had been so high, at ...

7

Actually, Ralph Vince's Leverage Space Trading Model does utilise draw down. A short introductory pdf is available here, and the R-forge package is here. Briefly, a genetic algorithm is used to model the maximum expected portfolio return based on a joint probability distribution of the portfolio component returns, subject to an overall maximum draw down ...

7

What you refer to as the 99.5th percentile is known as the "Value-at-Risk." You are correct that you will need to make a distributional assumption, and there is a popular and well-researched approach to this problem, though I'm not certain it could be called "standard." I would recommend you use the "truncated Levy flight" distribution. James Xiong at ...

7

You are absolutely right, I would say that how the interview question was posed and the example given is very misleading, if not outright incorrect. Here is why: Hedging does not increase your risk in this particular example: You take on delta exposure by buying the short dated option outright. Thus buying/selling underlying (put/call) in any case will ...

7

Note that $\beta$ is the coefficient of the portfolio regressed on the benchmark. That is \begin{align*} r_P = \alpha+\beta r_B + \varepsilon, \end{align*} where $\varepsilon$ is the residual. The standard deviation of the residual is called the residual risk. Specifically, \begin{align*} std(\varepsilon) &= \sqrt{var(r_P-\beta r_B-\alpha)}\\ &=\sqrt{...

7

What happened was totally unexpected end of peg against the euro @ 1.2CHF regime that Swiss central bank aborted. See some articles about it. As far as I know nobody in the markets knew, there was no indication whatsoever.. In terms of management, I'm afraid lots of people got heavy losses, particularly banks (Austria, Poland, Hungary) - lots of Swiss loans ...

6

Meucci covers this example precisely in his paper "Fully Flexible Views: Theory & Practice". You can find his code here for three examples related to the paper. The Butterfly Trading example covers the CVAR scenario.

6

This is the equity premium puzzle. (See that article for references.) My thoughts are that individual investors are rational to be risk-averse and demand a premium for bearing a type of market risk that cannot be diversified away. This risk is actually worse and more insidious than it appears, because "personal" circumstances tend to correlate in ...

6

I am a risk taker and I can say with confidence that you will never convince those individuals, you cited in your question, that they incur too much risk, because there will always be certain traders who prefer lottery tickets over longevity with the same firm (running high risk books unfortunately in the current environment runs equal to a free option; blow ...

6

Risk-free rate is that you get for letting someone else use your money in a riskless manner. Suppose we live in a world where there is no risk whatsoever. In particular, if you lend someone \$100 there is 100% certainty that he will pay you back in a year. Before the pay date, he can do whatever he wants with your$100, while you have no access to it. Even ...

6

The risk neutral drift is the risk free rate for an asset with no dividends, no cost of carry, no repo cost, etc. Otherwise the drift has to be adjusted to take these into account, and the easiest way to do it (when available) is to use forwards (equal to the expected asset value under the forward measure) or futures (equal to the expected asset value under ...

6

Different portfolio risk decompositions answer different questions. Before discussing what method to use, first ask why you want a decomposition and what definition of risk are you using. Is the point to examine how portfolio return volatility is affected by a tiny change in portfolio weights? On the other hand, if the point is to make a statement like, "30%...

6

Just a small addendum to @noob2's answer. The discrete shape of $\lambda$ is: $$\lambda \approx \frac{V_1 - V_0}{S_1 - S_0} \times \frac{S_0}{V_0}$$ which can be rewritten as $$\lambda \approx \frac{\frac{V_1 - V_0}{V_0}}{\frac{S_1 - S_0}{S_0}}$$ which is as @noob2 said just the ratio of the relative returns for option and stock.

5

Via Liquidity Horizons $LH$ (which have to be taken into consideration anyway when modelling for $Basel_3$) as function of the specific concentrations $c$'s. Increasing the effective maturity of the contract, $M_0+LH_0$, by a quantity proportional to its concentrations with respect to different slicings magnifies the credit risk. $M_0$ is the maturity ...

5

I asked this question 6 years ago, and in the meantime I came across this little volume: Lévy Processes in Finance: Pricing Financial Derivatives by Wim Schoutens (2003).

5

With minimum variance, the covariance matrix does not change when you change the holdings. So all the optimizer needs to do is change the weights. This makes it easy to calculate the gradients. To construct the drawdown statistic, you would need the distribution of returns in each period to your horizon. You would then need to calculate the path of profits ...

5

It doesn't make sense to use option price series data for computing option risk anyway. Since they are derivatives (i.e. their value is derived from other securities) it is more basic and reasonable to handle the underlying risks. As hinted by John, the risks to an option portfolio are generally considered in the context of inputs to a pricing model (which ...

5

Edited Comments: Sharpe Ratio covers both future and historical time frames (as @Freddy points out). Referencing the "Geometric Return and Portoflio Analysis", for the historical calculation, you want to make as few assumptions as possible (in my opinion). Let $m_i \triangleq$ the monthly return for period $i$ and $r_t \triangleq$ annual return, for $i\... 5 I think what you are missing is simply the Vega-Gamma relation in the Black-Scholes model. Namely: $$Vega = \frac{\partial v}{\partial \sigma} = \sigma(T-t)S^2 \frac{\partial^2 v}{\partial S^2} = \sigma \tau S^2 \Gamma$$ Plugging this into your coverage error, you get its expression in terms of the Vega which is the most natural measurement of your ... 5 In utility theory the basic assumption is that$u(c)$is strictly monotonically increasing in wealth: people prefer more over less. Hence,$\forall c, u'(c) > 0$. The second assumption is that the amount of utility added, as$c$increases, diminishes, so$\forall c, u''(c) < 0$. Combining these two observations we have that$\$\forall c, A(c) = \frac{-u'...

5

Try to give David Spiegelhalter a read/listen to David Spiegelhalter's work and research. He is a statistician and a Professor of the Public Understanding of Risk at Cambridge England. Rather than new ways of calculating risk, he looks at ways of communicating risk to a general public that doesn't have any knowledge of stats. I Linked an interesting video-...

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