Questions tagged [risk]

The possibility that a negative event (such as a loss) will happen.

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1answer
97 views

Should I include zeros in downside beta calculation?

Downside beta is the beta coefficient for an asset and a benchmark restricting benchmark returns to be less than a given value. Let’s assume zero for simplicity. We have: If we have returns in period ...
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1answer
75 views

How do I estimate the factor sensitivity in a Vasicek Single Factor Model?

I understand the formula of an asset return for an obligor i is given by the following: $$A_i = \sqrt{w_i}*Z + \sqrt{1-w_i}*\epsilon_i $$ My question is - How do I calculate $w_i$? I have the PD, LGD ...
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37 views

Does the interval of a portfolio's returns affect Sharpe and Sortino? If so, what's the gold-standard interval?

I'm currently creating a backtesting script and I've got to the point of calculating risk metrics. It seems like the interval (daily, weekly, or monthly) I use for returns heavily changes the ...
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82 views

Practical implications of Andy Lo paper on Sharpe ratio using quarterly returns?

I am hoping to determine the practical implications of the Andy Lo paper criticizing the use of a scaling factor in converting periodic Sharpe ratio to annualized Sharpe ratio. I am particularly ...
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2answers
101 views

IRS - sensitivity to estimation (projection, coupon) curve and discounting curve

The mark to market of an interest swap that is close to zero (e.g., at the swap's inception) has more sensitivity to which curve - the estimation (projection, coupon) curve or the discount curve? And ...
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304 views

Quarterly Survival rate given there is a Quarterly Probability of Default

I am trying to calculate the Quarterly Marginal PD. I have calculated it as given in the below image but I am thinking about whether the Survival rate calculation is making sense or not. The ...
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59 views

Ruin theory with infinite-mean Pareto-distributed claims: how to characterize the ruin time and the reserve prior to ruin

Consider the Cramér–Lundberg model $$\hspace{8em}R(t)=u+c\,t-\sum_{j=1}^{N(t)}V_{j}\,,\hspace{8em}(1)$$ where $c$ and $u$ are positive constants, $N(t)$ is a Poisson process with a rate $\lambda$ (in ...
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65 views

Optimal active risk

Can someone help me prove the statement or share a link of the proof - "The optimal amount of active risk is the level of active risk that maximizes the portfolio’s Sharpe ratio. This optimal ...
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1answer
78 views

Question in convex arbitrage [closed]

In convex arbitrage, we say that if the convexity of call(put) price as a function of the strike is violated, we can have arbitrage strategy. For instance, $$ C_{K_2}\geq \lambda C_{K_1}+(1-\lambda) ...
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58 views

Risk sensitivities of equity TRS

If we go short on an equity TRS (as in we sell the swap and pay the equity returns). Is it correct to say that we are: -Short spot -Long borrow cost -Long interest rate (the rate benchmark of the ...
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75 views

Why is the interest rate risk secondary for a vanilla equity option?

Consider the vanilla payout: $Max(S(T)-K,0)$ priced under the RN measure as: $E[e^{-rt}Max(S(T)-K,0)]$ which under no dividend/borrow assumption equals $E[e^{-rt}Max(S(0)e^{rt}X(T)-K,0)]$ for $X$ ...
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1answer
55 views

Identity of recent books on stock market & risk

Apologies if this seems out of place, but a couple years ago I read several popular books written in the last decade by a single author who was trying to disabuse readers of several fallacies ...
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28 views

How to find percentage of FX exposure hedged through financial statements

I am analyzing a company's annual report, and wish to find the percentage of FX exposure they have already hedged. I have the following information: The net FX exposure for 4 different years The ...
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1answer
34 views

Price of a floating coupon bond with issuer credit risk and recovery rate

I need help. I have an assignment for an exam where i have to compute the price of a portfolio composed by floating coupon bonds taking into account the issuer credit risk and the recovery rate in ...
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1answer
257 views

Quick rule of thumb for DV01 and CS01 calculations

If someone tells me there is a IRS and a CDS both with 10M notional and 5y maturity, is there a reliable quick calculation that I could easily do mentally to approximately calculate their ...
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63 views

Why is infimum chosen to define value at risk as opposed to the minimum?

I believe that the VaR is defined as the infimum of the generalized inverse of the CDF of the loss function (something like that, please correct accordingly): $$\text{VaR}(\alpha)=\inf\{x: F_L(x)\geq \...
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32 views

Where can I get historical updates to equity risk models (e.g. Barra)?

In risk models (such as Barra), new factors are added over time, and the model structures are also changed over time. I hope to get as much information on historical changes as possible. Apart from ...
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1answer
97 views

Non financial risk management

I am looking for some discussion papers, research insights on the Digital risk for fintech companies, bank etc. what they should. consider when offering their services (banking, lending etc.) ...
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2answers
135 views

Dependence between Credit Default Risk and Credit Spread Risk

I am trying to understand the difference and similarities between Credit Spread Risk and Credit Default Risk. Here is brief (and not all too precise) definition. Credit Spread Risk: Losses due to ...
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32 views

How to use CAPM model to calculate expected value of portfolio?

Let's assume that vector $(R_1, R_2, R_3)$ has multivariate normal distribution $N(\mu, \Sigma)$ where $\mu = (2, 6, 4)$ and $$\Sigma^{-1} = \begin{bmatrix} 2 & 2 & 2\\ 2 & 4 & 4 \\ 2 &...
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1answer
298 views

Realized Variance (realized volatility)

I'm confused about realized variance. I roughly know the theory around Ito Calculus and quadratic variation and integrated volatility so I understand what realized variance measures (even though as ...
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19 views

Capital Charge or Capital add on for Concentration risk using Model-free measure standardised HHI (Herfindahl Hirschman Index)

I am looking to calculate the Capital Charge or Capital Add on for Concentration risk using standardised approach using HHI Below is the HHI index calculation What is procedure to calculate the ...
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65 views

Sharpe ratio differs from Tradingview

I tried to backtest a simple strategy on TradingView, it made 6 trades with these results: Now I want to calculate Sharpe ratio using definition provided by TradingView. So, my daily returns(...
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61 views

Interest rate risk calculation for Banking book

There is a detailed discussions on the Interest rate risk for Banking book. For Floating rate bond, this states like below - such positions generate cash flows that are not predictable past the next ...
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1answer
67 views

Joint probability of default

Had a couple of questions from Jorion's FRM book (5th edition, page 438, Table 18.2 shown below). The book has a very stylized example as shown in the table below. The example shows how to calculate ...
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23 views

Estimate of loan risk due to change in income

Disclaimer: despite working at a bank, my background is in data science and not in quantitative finance. I'm very likely to miss certain technical terms of the domain and if that's the case, I'd ...
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30 views

Statistical Inference of Variance Risk Premia

Good afternoon, I am currently following Carr and Wu (2009) to compute variance risk premia from options written as (RV-EV)*100 for the payoff of a long var swap position. Now I want to see whether my ...
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2answers
53 views

What happens if my risk factor caught by statistical risk model using PCA turns out to be totally different from other PM's risk factor? [closed]

In order to explain systematic risk we use risk factors and I've learned that since they try to explain 'systematic' risk, risk factors are relatively well-known. However, what happens if the risk ...
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2answers
153 views

Deriving the risk-aversion coefficient

By considering the parametrised formulation of the mean-variance criterion by Markowitz, the risk aversion coefficient $\lambda$ can be derived as follow. As suggested by Arrow and Pratt, given the ...
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86 views

What are some advanced methods for bond risk transformations?

Consider a portfolio of bonds within a given yield curve (e.g. Gilt curve), consisting of positions in every bond in the curve. I'm looking for ways to transform the risk of the portfolio into ...
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1answer
80 views

Equivalence of Standard Deviation and Variance as a risk measure - WRONG?

In Modern Portfolio Theory, I often see that people seem to view Standard Deviation and Variance as equivalent. Example from Markowitz himself: "Thus far I have used the standard deviation ...
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1answer
76 views

VaR and Expected Shorfall estimations with negative shape parameter of a GPD (Extreme Value Theory )

So im trying to replicate an code from the Quantative Risk Management Book (https://github.com/qrmtutorial/qrm/blob/master/code/09_Market_Risk/09_Standard_methods_for_market_risk.R). But when i try a ...
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37 views

Implications of modeling operational risks without frequency distribution

When modeling operational risk, the Loss Distribution Approach (LDA) is widely used. Usually, we model the loss frequency distribution and the loss severity distribution and then aggregate both to ...
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2answers
110 views

Does "risk premium" imply a difference in expected value?

I'm trying to understand the term "risk premium". I keep seeing statements like this (from Investopedia) "A risk premium is the investment return an asset is expected to yield in excess ...
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2answers
791 views

Knightian uncertainty versus Black Swan event

I struggle to understand the difference between Knightian uncertainty versus Black Swan event. If I understand at least the basic premises, both views say that uncertainty is different from risk, and ...
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1answer
76 views

Estimating delta of VX futures to S&P 500

I'm trying to think about the right way to estimate the delta of a VX contract to the S&P 500. VX futures are on the VIX index, which is a basket of S&P 500 options. By extension, VX and ES (E-...
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457 views

FX Delta of a cross currency basis swap

I would like to understand in which case there is a presence of FX delta risk factor when trading a Cross-currency basis swap. By FX Delta, I mean the sensitivy of my swap PV with respect to FX Spot ...
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2answers
87 views

10-day VaR for a portfolio

So, Bank ANZ owns a portfolio of options on the USD/GBP exchange rate. The delta equivalent position of the portfolio is GBP 56.00. The current exchange rate is 1.5, with a daily volatility of 0.7 ...
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1answer
53 views

Calculation of Regulatory Capital

As per my understanding, the Regulatory capital for a Financial institution is calculated as sum of ...
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109 views

Portfolio Risk Contribution

I came across a paper that shows calculations for two types of portfolio risk contribution. The first shows "Asset risk contributions" and the second shows "Correlation-weighted asset ...
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4answers
117 views

Where can I find a current tail risk indicator?

The definition of tail risk (risk of 3-standard deviations movement) seems to imply there would be a current market indicator for this. Is there such an indicator available somewhere?
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2answers
168 views

The best "risk measure" for an investor who does not want to lose any of his seed money

Question There is an investor who is afraid of losing any of his seed money (initial investment). Variance of investment returns is not a problem to him. He is willing to take variance as long as he ...
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52 views

What is relationship Risk,Market Price of Risk and it's sign?

Now I'm studying this textbook ( Fixed Income Securities by Veronesi ). But this page gets me some trouble. I know that yield and Bond Price have negative relationship. But in this image, it says ...
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1answer
207 views

Monte Carlo simulations of correlated stocks by Geometric Brownian motion

I am trying to simulate using a Geometric Brownian Motion process three autocorrelated stocks. In particular, I need to simulate three different matrices with 1000 scenarios each using a Monte Carlo ...
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80 views

Show that portfolio's percentage contribution to loss (PCL) equals PCR (risk)

I came across this question during self study on a quantitative book (Question 3.6 on Page 75 of Quantitative Equity Portfolio Management: Modern Techniques and Applications By Edward E. Qian, Ronald ...
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35 views

Is there no fix to improving portfolio risk estimation under small sample size?

When asked if copula are needed to calculate portfolio Value-at-Risk, it is said that "You can use historical method if you have sufficiently enough data". But actually copula are also ...
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1answer
72 views

Risk-Neutrality: Discount factors of the $P$ world according to risk preferences?

I am coming to terms with the connections between the so-called $P$ world and the $Q$ world. In my understanding, the risk-neutral measure $Q$ induces a probability space under which investors are ...
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2answers
84 views

Industry or academic standard frequency to report the return, standard deviation, and Sharpe ratio?

Everyone (funds, banks, academics, financial information sites etc.) reports the annualized return, standard deviation, and Sharpe ratio. Yet we never get to know what the basis of their computation ...
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1answer
53 views

Why is standard error used to show diversification effect for unsystematic risk?

quite long text incoming, sorry for that: While reading a corporate finance textbook, i came across a section describing the effect of diversification as well as the systematic and unsystematic risk. ...
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1answer
225 views

Are momentum returns negatively skewed?

In the academic literature, I found that momentum returns are negatively skewed (e.g. Daniel and Moskowitz, 2002). As far as I understand, this usually happens when the "past losers" rebound ...

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