# Foundational equations or concepts of Finance

The following is paraphrased from: Fundamental equations in economics

For the other sciences it´s easy to point to the most important equations, inequalities, propositions or concepts that ground the discipline. If I want to explain Finance to a physicist say, what are considered to be the most fundamental, foundational or important equations, inequalities, principles, propositions (theorems, lemmas, etc) or concepts that underly the subject which I should introduce and attempt to explain?

My guess: Fundamental theorem of asset pricing or some Pricing Principle, but that's coming from a mathematical finance background. Would people coming from a corporate or personal finance (or whatever else finance is out there) background say something similar?

And if general finance is not necessarily on-topic here then I guess answer with financial economics.

• I would say the CAPM is a good way to introduce him to finance ! May 9, 2016 at 1:03
• Many people see finance as a branch of economics and call it financial economics. So the same basic principles of supply and demand, competition, incentives, etc. are at work. May 9, 2016 at 13:26
• @AlexisL. or her. thanks
– BCLC
Jul 9, 2021 at 12:28

Considering this is an Economics Stack Exchange site, I’m going to answer in the spectre of Financial Economics. These are the most foundational equations and ideas of Financial Economics to understand more complex applied or academic research.

1. Gross yield

The gross yield is the yield on an investment before the deduction of taxes and expenses. $$1+R_{t+1}=\frac{P_{t+1}+D_{t+1}}{P_t}$$ $R_{t+1}$: net yield $P_{t+1}$: price of the financial asset $D_{t+1}$: dividend

2. Present Value

Present value ($PV$) is the current worth of a future sum of money or stream of cash flows given a specified rate of return. $$PV=\frac{FV_n}{(1+R)^n}$$ $FV$: future value $R$: interest rate

3. Gordon’s growth model

The Gordon growth model is used to determine the intrinsic value ($V_0$) of a stock based on a future series of dividends ($D_0$) that grow at a constant rate ($g$). $$V_0=D_0 \frac{1+g}{R-g}$$ $R$: interest rate

4. Bond pricing The price of a bond is the sum of the present values of all expected coupon payments plus the present value of the par value at maturity.

$$P_{bond}= \sum_{t=1}^T \frac{\text{Interest}}{(1+r_{it})^2}+\frac{\text{Par Value}}{(1+r_{iT})^2}$$

5. Duration

A measure of the sensitivity of the price (the value of principal) of a fixed-income investment to a change in interest rates. Given the relation between present value, future cash-flow and yield to maturity:$$PV=\frac{\sum CF_t}{(1+YTM)^t}$$ The second order Taylor polynomial is the following: $$dPV=\underbrace{ \left( \frac{dPV}{dYTM} \right)dYTM}_{\textbf{Duration}}+ \underbrace{\left( \frac{1}{2} \right) \left( \frac{d^2 PV}{dYTM^2} \right)dYTM^2}_{\text{Convexity}}$$

$YTM$: yield to maturity

6. Convexity

For any given bond, a graph of the relationship between price and yield is convex. This means that the graph forms a curve rather than a straight-line (linear). The degree to which the graph is curved shows how much a bond's yield changes in response to a change in price.

$$dPV=\underbrace{ \left( \frac{dPV}{dYTM} \right)dYTM}_{\text{Duration}}+ \underbrace{\left( \frac{1}{2} \right) \left( \frac{d^2 PV}{dYTM^2} \right)dYTM^2}_{\textbf{Convexity}}$$

A premium that investors will demand when any given security cannot be easily converted into cash, and converted at the fair market value.

8. CAPM (Capital Asset Pricing Model)

A model that describes the relationship between risk and expected return and that is used in the pricing of risky securities. It can be estimated by simple OLS: $$ER_i=R_f + \beta_i(ER_m-R_f)$$

$ER_i$: expected return of portfolio $i$, $ER_m$: expected return of the market portfolio, $R_f$: risk-free portfolio, $\beta_i$:CAPM-beta of portfolio $i$

• thanks Übel Yildmar!
– BCLC
Jul 9, 2021 at 12:25

For corporate finance, a big question is "How does activity X by firms affect shareholder wealth?" Irrelevance propositions (eg Modigliani and Miller) argue that under some conditions, a particular activity leaves shareholder wealth unchanged (eg debt levels are irrelevant to firm value). Complete markets make it so that disagreements about payout policy can be "traded away".

I wouldn't call finance a science. There aren't really analogs of physical constants, for example.

• thanks manofbear!
– BCLC
Jul 9, 2021 at 12:25