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4

No doubt about it: Tick charts are always grouped in Fibonacci numbers! In all seriousness, I have no experience with tick charts. I do have experience with pseudo-science, however, and believe devotion to pseudo-science to be the most likely explanation. Like the other folks who've contributed answers, I gleaned some information off the web. This ...


3

Here's a theory for why! The number of ticks $G_n$ in the time frame has to be an integer The ratio of observed ticks to predicted ticks should be roughly a constant $\theta$. That ratio $\theta$ should satisfy $1<\theta<2$, as the time interval that you have observed $[0,G_n]$ should be just a little longer than the time interval that you are ...


2

You will be disppointed. Most people place their pending orders at Fibonacci levels because they have been taught (by idiots) that there is something about those levels. Now, the herd has turned this into self-fulfilled prophecy: the more traders place their orders at those levels, the more that will look like "but there must something true about it, ...


2

$72$ is an approximation, not an exact value. It is handy because it has so many factors of $2$ and $3$ it is easy to divide into. It comes about because it is close to $100 \cdot \log(2) \approx 69.3$. If the compounding were instant, the correct value would be $69.3$, but because the compounding is annual you want a number a little higher. As the ...


2

The Rule of 72 isn't exact. It's a rule of thumb. The actual doubling time for a periodic growth rate depends on the periodic rate $r$ and the number of periods $n$: $$(1+r)^n = 2.$$ As $r$ varies from $1$ to $15% percent, the product that results in a doubling time varies a bit, but not much. If $r=0.01$ then $$1 \times n = \ln 2 / \ln 1.01 \approx ...


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A recommended book which covers most of your topics is Options, Futures and Other Derivatives - John Hull. Regarding simulation methods, I would suggest Monte Carlo Methods in Financial Engineering - Paul Glasserman.. Both books are a good starting point.


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This is a Binomial_series $$(1+i)^n= 1 + ni +\frac{n(n-1)}{2!}i^2 + i^3(...)$$ If $i$ is 'small' (e.g. $ni < 0.1$) you can 'omit' higher powers of $i$. Example with two decimals $n=10,\, i=1\%=0.01,\,$ and for simplicity $C=1:$ $$(1+0.01)^{10} = 1.104622\dots \approx 1.10$$ $$1 + 10\times 0.01 +\frac{10\times 9}{2}0.01^2 + \dots =1 + 0.1+0.0045 +\dots ...


2

You have a geometric sum. The $n$th term is given by $$\sum_{m=1}^n i^m =\frac{i-i^{n+1}}{1-i}=i\frac{1-i^n}{1-i}$$


1

What I think you are looking for is the present value of a growing annuity. Your problem says that your nominal interest rate is 6%, you will have to find the effective interest rate: $$r=(1+\frac{r_n}{12})^{12}-1$$ $$0.061678=(1+\frac{0.06}{12})^{12}-1$$ Then you can find the present value of the annuity: ...


1

To understand how to proceed you have to dispense with the formula and look at the derivation of the tangent portfolio from first principles. The multiobjective model is $$\begin{array}{ll} \text{maximize} & (\bar{R}^T x + R_f x_f, - \tfrac{1}{2} x^T V x) \\ \text{subject to} & \vec{1}^T x + x_f = 1 \end{array}$$ The zero risk solution is of course ...


1

Mathematically, the problem is a bit ill-defined. We're not certain of your goal: Do you care about your strategy's expected value of winnings only? Or do you want to end up above $2000 at the end of the interview but are very averse to busting? Etcetera. We're also not certain what sorts of prices you're going to be given in the future. That said, it ...


1

I imagine the $.10\%$ quoted rate is annual. So the monthly rate would be $\frac{.10\%}{12}\approx .0083\%=.000083$. That should come out to about $8.3$ cents per month interest on $\$1000$.


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The underlying mathematical reason is that when $|x|$ is small, we have $$\ln(1+x) \approx x$$ So suppose the compound annual interest rate is $\frac{r}{100}$, we want to find $n$ such that $$(1+\frac{r}{100})^n = 2$$ which gives $n = \dfrac{\ln 2}{\ln(1+\frac{r}{100})} \approx \dfrac{\ln 2}{r/100} = \dfrac{100 \ln 2}{r}$ Then we replace $100 \ln 2$ by ...


1

On investigation on the topic of tick charts, I believe I may have one plausible explanation. Tick charts are essentially a variation in the $x$ axis variable - instead of plotting against time, you plot against trades... but since it isn't feasible to try to make out the fine detail, they plot after every $n$ trades. And a common choice for $n$ is 233. ...


1

Let's go through the basics. You are receiving an annuity of $\$78$ each quarter for $40$ quarters. The interest rate is $8\%$ compounded quarterly, which is $2\%$ effective quarterly. Let $P_i$ denote the present value of the $i^{th}$ payment. $P_1 = P(1+i)^{-1} = 78(1.02)^{-1}$ $P_2 = P(1+i)^{-2} = 78(1.02)^{-2}$ ... $P_{40} = P(1+i)^{-40} = ...


1

Start with initial amount $A$. At the end of one year the value will be $A \left (1+\frac r {100} \right)$. At the end of two years the value will be $A \left (1+\frac r {100} \right)^2$. At the end of n years the value will be $A \left (1+\frac r {100} \right)^n$. You want the amount to double, so it will be $2A$. We therefore need to solve $2A=A ...


1

The process that is modeled by the rule of 72 is Compound Interest, which works like this: during each compounding period, the money in your account increases by some percentage; this increase is pulled back into your account, where next time around, it too will be increased by some percentage. So if you have $\yen1,000,000$ in your account and it grows at ...



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