# Tag Info

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{... • 8,421 12 votes Accepted ### 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 ... • 1,399 4 votes Accepted ### 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 ... • 6,064 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 ... 3 votes Accepted ### 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: $$y = -\ln (z)$$ • 5,043 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 ... • 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 ...
• 989
Accepted

### 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 ...
Accepted

• 1,086
Accepted

### 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{...
• 21.2k
Accepted

• 6,064
Accepted

### Using CAPM to derive the following

The standard formula for Capital Asset Pricing Model is: $$\bar{r} = r_f + \beta \cdot ( \bar{r_m} - r_f) \quad (1)$$ in which: \bar{r} \textit{ - ...
• 136

### 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}{\...
• 193

### 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. ...
• 17.2k
Accepted

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)^... 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 ... • 1,643 2 votes Accepted ### 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: ... 2 votes Accepted ### 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). ... • 6,737 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. 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 ... • 1,409 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 ... • 370 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. • 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 ...
• 236
1 vote
Accepted

### 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.
• 17.2k

Only top scored, non community-wiki answers of a minimum length are eligible