Basic mathematic problems for finance

This thread is about mathematical problems, questions, solutions and general considerations in finance/economy/trade.
The aim of the discussion is to increase knowledge about the mathematical aspects of
finance, and the interconnections between various assets as well as providing problems with solutions

Please share your information about what you think is the most important to calculate or understand in order to be a good personal money manager, successful trader, statesman or even banker. Share any method/study you invented and what it aims to investigate. And highlight your contribution with a underlining in bold at the beginning of your 1st message so people have it easier to scroll through the thread to the topics they are interested in, as well as finding the start of a topic.

Example topics: (Q&A) Interest rates -How to calculate profit of treasury bond (Theory/T) Monetary history (Calc) Tax on profit
(Idea) Pip limit for greedy A basic solution to no overtrading. (Roleplay) How me as a statesman can squeeze the pennies out of people
(Q) What profit increase as a new trader should i expect at this leverage? and so on... to exemplify.
This way people can save time, and it is easier on the eyes. I hate when one has to read hours through a thread and never get to the understanding we seek.
Everyone has different levels of knowledge, thus if this becomes a thread of many pages i don't wanna tell somebody: "You should read from the start!" i rather tell them they can read what they like.

Please contribute with any of your ideas or solutions!

(Q&A) Taxes on profit
Bob buys 10 Tesla stocks for the price of 100 dollar/stock on May the 4th. In September the 14th he buys 100 Tesla stocks for 60 dollar/stock.
Bob decides to sell all his stocks a few days before christmas to the price of 80 dollar/stock.

Bob calls the tax office and asks how he is to file his capital gains/capital losses and how much tax he has to pay on the deal.
The IRS-lady tells Bob: "30% tax on all your gains and 70% deduction on any losses, you should use the "averaging method" for the stock
to calculate the profit of all transactions in Tesla stock.

a) How many Tesla stocks did Bob buy?
b) What was the average price of Tesla stocks?
c) Multiple the average price with number of stocks bought
d) How much tax will be paid by Bob after reporting to IRS? or will he receive a deduction?
e) Did Bob make a profit or loss, if so how much?

(Q&A) Basic teaser
What is the sum of all numbers from 1 to 100?

I do not work in the financial sector, but I will try to answer these questions.
1. 10 + 100 = 110 Tesla stocks.
2. (10 x 100) + (100 x 60) = 1000 + 6000 = 7000 dollars spent on 110 Tesla stocks. The average price is 7000/110 = 63.6363 dollars.
3. 63.6363 x 110 = 6999.993
4. Bob spent 7000 usd to buy 110 Tesla stocks. Bob sells all his Tesla stocks to the price of 80 dollar/stock. 110 x 80 = 8800 usd. 8800 - 7000 = 1800 usd gains. 1800 x 0.3 = 540 usd taxes.
5. After the taxes Bob made 1800 - 540 = 1260 dollars of profit.

All correct. In some countries you have to account for currency gains/losses too.
Well done!

[Formula]
Fair value calculation of forex future.
F= Fair value
Spot= Spotprice
T = Time to maturity in years

𝐹=𝑆𝑝𝑜𝑡×𝑒^(local interest rate−foreign interest rate)×𝑇

Example of maturity date calculation: maturity in 18 months: 18/12 = T = 1.5
maturity in 6 months: 6/12 = 0.5.

Moving stops + moving out of the range + impulse larger than the average range expansion to the opposite of move 200 periods ago.
Price/Price change of the same time period_199 bars ago, Price/Price change of the same time period_198 bars ago, Price/Price change of the same time period_197 bars ago...
Price/ price change of the same period vs reference price/price change of time period... x10-25 reference.

We are in 2022 and there is alot of market turmoil. You spot a correlation between the dollar and the stock market.
Every time the dollar goes up the market goes down.
The correlation start to fade as we go into 2023, now the market and dollar can go up at the same time.

a) What would be the simplest explaination for market going down when dollar goes up in 2022?

b) What would be the accepted and mainstream opinion about why this happens? If you already have learned it.

c) If we use the simple explaination-approach again, why are the market not selling off any more when the dollar goes up?

d) and again a more complicated answer to c) what is the mainstream opinion?

The average is 50.5 [(100+1)/2] and there are 100 of them, so one would expect it to be 5,050? What’s the catch?

The catch is that everything shall be easy here, just like in the heat of the moment of trading.
Through practice of simple things one stores it in long term memory and frees the working memory.

This is why geniuses fail, they never go back to easy tasks and repeat them - it's beneath them.
And also why average people fail, since they by social pressure are driven into competition and if they lose they will avoid the hard task or subject in the future, basic logic and mathematics is the most common.

Of course i am in no position to teach others, i am modestly successful myself. But this is my philosophy; to divide life and trading into components and to repeat them for building strength - thus back to basics.
I may occassionally write something advanced with many steps in here, but that's just cause nobody visits and i want to repeat the concept at a later date.

Feel free to make it a problem though or relate it to trading. How about the above problem i described? have you thought about a simple explaination for the Dollar correlation? there is no right or wrong of course, just an expression of opinion or weathering a thought.

Should also add here probably that if you use e (Exponent), you should also use continuously compounded rates (convert if necessary)

I most have made an error. Can you added the correct formula with the right input sources? it was hard to come by this information so i couldn't compare it with other sources.

You solve an equation e^R = 1+r, where R - continuously compounding rate, r - interest rate compounded annually.
Taking natural logarithm on both sides: R =ln(1+r). So if annually compounded rate is 10%, then R = 9.53%

Key thing to not to not confuse yourself is that R and r are just different measures of same concept, namely interest, like meters and kilometers for distance.

Reminder and advice to future self:
Embrace the gray. Remember that if you mix all other colors together, it will always end up gray or any shade there of, thus every color visible or invisible is connected to the gray.
What is the gray? it is an area you often avoid and who is in opposition to most humans feelings, thought patterns and actions. One can seemily have mastered the gray as there was skills developed from a line of work, which might make the impression that one is disciplined, and have lived by the gray. But this is not true.
They might have made it into a habit, and an automatic behavior thus making it rather effortless and thoughtless on their part, but for the viewing party it is seen as strength and discipline, while it just is the natural state of that person.

How can you develop your gray skills? = embrace the things you don't wanna do, approach the people you dislike or don't understand, take what you are comfortable with one step further.
If one has a strong gray side, one might approach any of the other colors with discipline and great enjoyment. But one focusing on only one other color will never develop it to a full extent or full understanding as everything is connected and every color offer edges to the other color.

Other ways that offers skills in the gray: Doing intense brain activity without sugar, or low sugar. Avoiding coffee during activities that requires energy. Static exercises. Being kind to a rude person. Giving money to someone else, while you need it or want it. Agreeing to do something you don't wanna do. Talk to uninteresting people. Cleaning the house.
The list can be made virtually endless, but as soon as it becomes an acceptable habit it is no longer that gray. One should write down recurring thoughts about matters who should be done, but for some reason isn't done. One should write down what one avoids, and one should go back to look at that long list one day and see which things is reoccuring.

Everything that is fun and done with ease is already developed. If you want to develop you need always to seek the Gray. One can cheat the gray by developing all other colors to extent, as it lays down a strong foundation. This way might make it easier for one to tackle an impossible task in the future.

Besides the gray: remember future self that you are best in the heat of the battle, were quick decisions have to be made and many calculations have to be made under stress. You already have a good track record proving this is true in real life, when you worked at emergency department. Always remember yourself and never try to be somebody else.
And always embrace people that are different, be kind to them and help them if you can.

Thoughts and lessons from the week

- Manage positions better or don't trade at all.
- Major shifts in end of month may cause alot of volatility, also major levels and shifts of policy(as of perceived by media regarding monetary policy)
- Go scalper when you identified a trading range and uncertainty, but do mind it requires time and concentration.

- There might have been a change in mechanism or correlations between the dollar and the other pairs. Should proably investigate if it is mechanical or sentimental. Other pairs might have taken over or became independant(Yuan/Yen?) the SOFR shall be fully implemented as of latest of June, find out if there is anyone who can translate it into trading.
- Find out which currencies use the old system(outliers)

Real rates = (Nominal interest rate -inflation)

This means purchasing power is lost, as the rate increase cannot keep up with the price increase.
Means that the rate increase doesn’t have desired effect, and the currency can lose more value due to disbelief of investors in the country’s ability to tackle economic difficulties.

Basic rules for each time: Adaptability and staying informed are crucial in trading

To maintain a stable currency and attract investment, it is important for countries to balance their monetary policies, address inflationary pressures, and ensure that the nominal interest rate provides a positive real rate of return, thus preserving the purchasing power of the currency.

This might be an issue with Central banks who might have destabilized the economy for the purpose to motivate the replacement of the old system with the new.
There are underlying demographic issues in the west which is not considered, and tax problems and overregulation. An already tight snare is tightened further.

Question is if these are old and useless methods just like TA in trading. We live more in a service-society today, and there is a lack of competition among more important goods/wares.

Wasn't the hyperinflated nations in South America mostly based on services for running the economy? how well did they manage to come out of an economic crisis with their rate increases and central bank policy?
I think i heard somewhere big part of their GDP is service.

Dealers recover their losses to profitable traders by widening the spread between bid & ask. Losing traders therefore pay more for their trading when dealers lose alot to profitable traders. Therefore there is collateral damage of profitable traders on unprofitable traders.
However this will hardly ever be noticed in a high liquidity asset such EURUSD or the pound.

draw a line to see
look where there is none, and where it’s gone
A place where there is none between same places it’s gone can at the right time weigh a ton.

A simple number for ease of doing business…