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3

The answer is that you may use an approach that includes IRR, but that's not a necessary component of what I would consider a good model. I have seen commercial tools that include them and those that don't. I have also seen practitioners set the variables in packages that include this approach, so that they were not a relevant component of the resulting ...


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IEX is an ATS. The ECN/ATS business is dominated by rampant and well known conflicts of interest. A part of the IEX value proposition from the beginning was to offer an alternative to traders who were disenfranchised by this market structure. If maker-taker rebates are part of your trading business model or if you engage in any strategy that could be deemed ...


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Assume the weights of the two assets are $w$,$1-w$ respectively;the expected returns and standard deviations are denoted by $\mu$,$\sigma$ with subscripts 1,2,p(for portfolio),i.e,we have $\mu_1$,$\mu_2$,$\mu_p$,$\sigma_1$,$\sigma_2$,$\sigma_p$.The correlation coefficent is $\rho$ Then $$\sigma_p^2=w^2\sigma_1^2+(1-w)^2\sigma_2^2+2w(1-w)\sigma_1\sigma_2\rho ...


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Since $Y=e^{(r-\frac{\sigma^2}{2})\tau + \sigma \sqrt{\tau}Z}$, then \begin{align*} xY > K \Leftrightarrow Z > -d_2, \end{align*} where \begin{align*} d_2 = \frac{\ln \frac{x}{K} + (r-\frac{\sigma^2}{2})\tau}{\sigma\sqrt{\tau}}. \end{align*} Consequently, \begin{align*} e^{-r\tau}\mathbb{E}\big(Y \mathbb{1}_{\{xY >K\}} \big) &= ...


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I think to gain intution you have to understand that the same agents that value the stocks will value the options. And agents compensate for volatility by demanding higher expected returns. Therefore you should ask: Why are stocks priced as they are in the first place? In your example, the stock with higher volatility has much lower expected return. This ...


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Yes and No. In the absence of arbitragers, the price of the option will be different for each speculator based on their drift expectations (and each speculator has a risk in his position and will limit his ability to trade large sizes to avoid bankruptcy) and the option price will converge to priced off a supply-and-demand driven drift expectation. ...


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Because you can hedge. Once you have delta hedged, the pay-off is symmetric about up and down moves so drift doesn't matter. Also the delta-hedged call and the delta hedged put have to have the same value since they have the same pay-off. (Put-call parity) Yet any argument that the call should be worth more because of drift says that the put should be ...


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Yes, for a short time horizon like 1 - 10 days, assuming $\mu = 0$ is fine. As you'd correctly pointed out, for 1 - 10 days (and referring to the link you'd referenced to), it scales linearly by $T$ (recall that $T$ is an annual number, so convert to a % number in reference to days), but volatility scales by $\sqrt{T}$ and so it is much larger than $T$ for ...


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This will depend on the definition of "return on the long run". If we define the annualized return on the long run by $\frac{1}{T}\ln \frac{S_T}{S_0}$ for a certain time $T$ in the future, then \begin{align*} E\left( \frac{1}{T}\ln \frac{S_T}{S_0} \right) = \mu-\frac{1}{2}\sigma^2, \end{align*} as claimed. Note that $\mu$ is the instant, or instantaneous, ...


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Trying to shed some light here: What we also see using this here, is that if returns are log-normally distributed, ie. $$ 1 + r = \exp(\mu + \sigma Z), $$ with $Z$ standard-normal, then $$ E[1+r] = \exp(\mu + \frac 12 \sigma^2) $$ holds. But the geometric mean $GM$ is given by $\exp(\mu)$ and we have $$ \log(GM) = \mu = \log(E[1+r]) - \sigma^2 /2 $$ and ...


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It is the same. With enough data, you could not reject the null γ1=β2. You could test that with simulation. See this with R: ## set.seed(12456) ns=500 t=1:ns D[]=0 D[t>.1*ns&t<.33*ns]=1 rm=rnorm(ns,.01,1.5) ri=0.01+1.2*rm+.15*D+rnorm(ns,0,.5) plot(ri~rm,col=D+2) #Model 1 summary(lm(ri~rm+D)) #Model 2 (m1=lm(ri~rm)) res=resid(m1) ...


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Yes leverage amplifies the exposure of equity to systematic risks. Just consider the standard textbook formula (Modigliani-Miller): $\beta_e = \beta_a \times (1+\frac{D(1-\tau)}{V})$ where $\beta_e$ is the sensitivity of the stock to systematic risk, $\tau$ is the tax-rate and $D/V$ is the leverage ratio. So beta (i.e. the exposure to systematic risk) ...


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Practically, it is very difficult to get a measurement of a stock's true drift while there are very well-documented processes to estimate volatility. It is therefore very convenient mathematically to select the risk neutral pricing measure that eliminates idiosyncratic drift. At its heart, Black Scholes constructs a dynamic, replicating portfolio for an ...


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Singer and Terhaar original paper can be found at this link. They do not provide an explanation about how to estimate this factor and just mention that both values provide a boundary. The CFA curriculum mentions that " For example, it has been observed that developed market bonds & equities are approx 80% integrated and 20% segmented.", however the ...


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A friend constructed an equal weight portfolio for a client that was constrained to a certain number of holdings. I don't mean less than 20 (less than or equal constraints are more common) but =20 holdings. He chose an ordinality based (sort) approach and he liked a paper, but I don't remember which one. Until then I hadn't thought about using the approach ...


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I can't comment yet on the topic due to my reputation level (so I will throw an answer up) but having just done my MFE capstone research on EVT implementation for VaR. According to my advisor who was a director of a quant research group at Citi before returning to academia, not many people are doing this. My research was to start collecting data comparing ...



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