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12 votes

Interview Question - Card betting

It all depends on your level of risk aversion and degree of intertemporal substitution. Let's assume you are risk neutral: Game is played once: you are willing to pay $6.5 = \sum^{N=12}_{i=1} \frac{...
phdstudent's user avatar
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12 votes
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Pre-requisite math books, to the pre-requisite math needed to become a front desk quant

Really you need a degree Reading any one book from the above will not set you up. Furthermore, you will find yourself trapped in a cycle, where really none of the books you suggested can be read in ...
oliversm's user avatar
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4 votes
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Joshi, Exercise 2.7 Concepts of Mathematical Finance

The idea is pretty much the same as the one used in the Breeden-Litzenberger result. You'll find many questions related to this here already, see e.g.: Prove that the butterfly condition is always ...
LocalVolatility's user avatar
3 votes

Does anyone know where to practice mental math for trader interviews in MC format?

I personally used the Secrets of Mental Math by Arthur Benjamin and https://www.tradermaths.com/. However, you should still practice fractions after using both resources as this is not well explained ...
Guyon Van Rooij's user avatar
3 votes
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Calculating coupon yield and continous compounding

Hint: Let $$z = \mathrm{e}^{-y} $$ That way you get a quadratic equation in $z$ (note that $z$ is positive) and then you can get back to $y$ using: $$ y = -\ln (z) $$
ir7's user avatar
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3 votes

Interview Question - Card betting

If the game is played in exactly the way you stated it, why would you ever bet more than 1 dollar? Assuming you bet 1\$, then you get 1\$ x value on card. And if you bet 12\$, you get 1\$ x Value on ...
Jesse's user avatar
  • 31
3 votes

How much shall we bet on head/tail with $1m bankroll?

I think you have it backwards regarding how much to bet if you play once vs. many times. The optimal amount to bet is given by the Kelly criterion as you said. But you should be MORE inclined to bet ...
roz's user avatar
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3 votes
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Given three stocks what is the fraction of each stock's risk is diversified away

In general, the variance of a portfolio is just $$\sigma_p^2 = \sum_i \sum_j w_i w_j \sigma_i \sigma_j \rho_{ij},$$ which intuitively makes sense since we are summing over all weighted standard ...
Forgottenscience's user avatar
3 votes
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Given two risky stocks calculate the rate of return, standard deviation, beta, and risk-free rate

a.) The market capitalization $m_{cap} = 100*\$1.50 + 150*\$2.0 = \$150 + \$300 = \$450$, so the weight of each asset is $1/3$ and $2/3$ respectively in the market portfolio. You don't need to find ...
Forgottenscience's user avatar
3 votes
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Mark Joshi, The concepts and practice of mathematical finance chapter 6 exercise 20,21

Note that \begin{equation} E\big[e^{\sigma \alpha \sqrt{T} N(0,1)}\big] = e^{\frac{\sigma^2 \alpha^2}{2}T} \end{equation} Hence $F_T(T)^\alpha$ will be a lognormal variable with expected value $F_T(...
Freelunch's user avatar
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3 votes
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Implied Expected Stock Return from European Option Prices

Note that \begin{align*} \frac{S_T-S_t}{S_t} &= \frac{S_T-K +K-S_t}{S_t}\\ &=\frac{(S_T-K)^+-(K-S_T)^+ +K-S_t}{S_t}. \end{align*} Then, \begin{align*} E\left(\frac{S_T-S_t}{S_t} \mid \mathcal{...
Gordon's user avatar
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3 votes
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Finding optimal trading of option on a foward

The optimal investment strategy depends on the investment goals, or equivalently your utility function (which the investment strategy is supposed to maximize). The forward will trade at $\mathbf{E}^*...
bhutes's user avatar
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2 votes
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Finding the extrinsic value of an option with conditions

Find the conditions under which: $E_{0}^{*}[\max (P_{T} - HR\times G_T, 0)] = \max (P_{0} - HR\times G_0, 0)$ We have a no-brainer solution - the condition that the drift and volatility of both $P$ ...
bhutes's user avatar
  • 1,006
2 votes
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Properties of Brownian motion and filtration, Exercise 6.22, Joshi Concepts and applications to mathematical finance

\begin{equation} \mathbb{E} \left[ \left. W_s \left( W_t - W_s \right) \right| \mathfrak{F}_s \right] = W_s \mathbb{E} \left[ W_t - W_s \right] = 0 \end{equation} The first step uses that $W_s$ is $\...
LocalVolatility's user avatar
2 votes
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Using CAPM to derive the following

The standard formula for Capital Asset Pricing Model is: \begin{equation} \bar{r} = r_f + \beta \cdot ( \bar{r_m} - r_f) \quad (1) \end{equation} in which: \begin{equation} \bar{r} \textit{ - ...
Jakub Siwiec's user avatar
2 votes

partial derivatives of multivariable function

No, this is in general not true. For example, consider \begin{align*} y(x)&:=x,\\ x(a,b):&=a+b. \end{align*} Then we have $$\frac{\partial y}{\partial x}=1$$ but $$\frac{\partial y}{\...
amars's user avatar
  • 193
2 votes

Interview Question - Card betting

To elaborate on my comment: with respect to questions 1 and 2, the distribution of the payoff for one game is discrete uniform with a mean of 6.5 and a SD of about 3.5 according to my calculations. ...
dm63's user avatar
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2 votes
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Why the variance of a process is $\left( \frac{dS_T^2}{dt}\right)^2$?

Because instantaneous variance can be written as follows: $V \left[ dS_t\right]=E\left[ \left( dS_t -E\left[dS_t\right] \right)^2\right]$ $V \left[ dS_t\right]=E\left[ \left( dS_t -f \, dt \right)^...
Magic is in the chain's user avatar
2 votes

How is hypothesis testing work in population sampiling?

This is pretty standard fare for a Stats 101 course, so as to rationale, etc. you might benefit from picking up a textbook or otherwise do some reading on this. In brief though, hypothesis testing ...
Chris's user avatar
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2 votes
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Determine the error term of SKEW-calculation

In the third equation they somehow did not put the 1/3 in front of the second ln-term. Without the 1/3, the equation looks at follows: ...
Wouter Kroneman's user avatar
2 votes
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Dice question - expected winnings of rolling dice $2$ times

Let's apply basic utility theory. Note that the expected utility is driven by the outcomes, their probabilities and the initial wealth $W_0$ of the gambler (see @Dimitri's comment to your question). ...
Kermittfrog's user avatar
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2 votes

Does anyone know where to practice mental math for trader interviews in MC format?

You could write your own. That would allow you to customize it as you wish, and have the double effect of practicing programming.
Acccumulation's user avatar
1 vote

Mental math method for large integer multiplication

I would calculate it as: $-4.41*2.86 = -(440*286+286)/10,000=-(400*286+40*286+286)/10,000=-(114,400+11,440+286)/10,000=-12.6216$ But this definitely is not the best way. I expended quite abit of ...
KaiSqDist's user avatar
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1 vote

Does anyone know where to practice mental math for trader interviews in MC format?

This is a personal fav of mine, you can customize the operations and range and then practice on different parts: https://arithmetic.zetamac.com/ I would also study tricks to make certain calculations ...
apocalypsis's user avatar
1 vote

Bachelier call option derivative w.r.t strike

I figured it out. the second source had a drift component in the SDE that i didnt have.
Jay's user avatar
  • 11
1 vote

How much shall we bet on head/tail with $1m bankroll?

For continuous play you generally want to maximize the expected log return (time average rate of growth under geometric wealth dynamics) conditional on not going bust. This is basically Kelly setup ...
safetyduck's user avatar
1 vote
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Price of every asset in discrete market model strictly increasing

Off the top of my head, if interest rates are zero or negative, then yes. Just borrow the purchase price and buy any asset. Sell later and pay off the loan. Otherwise no.
dm63's user avatar
  • 17.2k

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