toutes les formules de mathématiques financières pdf

5․2․ Internal Rate of Return (IRR) Formula

The IRR is the discount rate that equates the NPV of an investment to zero․ The formula is:

0 = ∑ (CF_t / (1 + IRR)^t) ― Initial Investment

Where CF_t is the cash flow at time t, and IRR is the internal rate of return․ Unlike NPV, IRR provides a percentage return, making it easier to compare projects․ It is widely used in investment analysis to determine profitability, as detailed in the PDF guide․

Risk and Return Analysis

This section explores the relationship between risk and return, focusing on the Capital Asset Pricing Model (CAPM) and portfolio risk management, as detailed in the PDF guide․

6․1․ Capital Asset Pricing Model (CAPM) Formula

The Capital Asset Pricing Model (CAPM) formula calculates the expected return on an investment based on its risk․ It is expressed as:
E(R) = R_f + β(R_m ― R_f), where:
– E(R) is the expected return,
– R_f is the risk-free rate,
– β measures the asset’s volatility relative to the market, and
– R_m is the market return․ This formula helps investors assess the required return for an investment’s risk level, guiding portfolio decisions and asset pricing strategies, as detailed in the PDF guide․

6․2․ Portfolio Risk and Return Formulas

Portfolio risk and return formulas quantify the relationship between diversification, risk, and potential returns․ The expected return of a portfolio is calculated as:
E(R_p) = Σ(w_i * E(R_i)), where w_i is the weight of asset i and E(R_i) is its expected return․ Portfolio risk, measured by variance, is:
σ_p² = Σ(w_i²σ_i²) + 2Σ(w_iw_jCov(i,j)), where σ_i² is the variance of asset i and Cov(i,j) is the covariance between assets i and j․ These formulas help investors optimize portfolios for desired risk-return profiles, as detailed in the PDF guide․

Financial Derivatives

Financial derivatives include options, futures, and forwards, essential for hedging and speculation․ Key formulas like the Black-Scholes model for options and futures pricing are covered in detail․

7․1․ Option Pricing Formulas (Black-Scholes Model)

The Black-Scholes model is a cornerstone in financial derivatives pricing․ It calculates the theoretical price of a European call option using the formula:

C = S₀ * N(d₁) ― K * e^(-rT) * N(d₂)

where S₀ is the stock price, K is the strike price, r is the risk-free rate, T is time to maturity, and N is the cumulative distribution function of the standard normal distribution․ The variables d₁ and d₂ are calculated as:

d₁ = (ln(S₀/K) + (r + σ²/2)T) / (σ√T)

d₂ = d₁ ― σ√T

This model assumes lognormal stock price distribution and constant volatility․ It is widely used for pricing options and understanding derivative risks․ For detailed insights, refer to the Black-Scholes PDF guide․

7․2․ Futures and Forwards Pricing Formulas

Futures and forwards are over-the-counter (OTC) and exchange-traded derivatives․ The pricing formula for futures is based on the no-arbitrage principle:

F = S₀ * e^(rT)

where F is the futures price, S₀ is the spot price, r is the risk-free rate, and T is time to maturity․ Forwards use a similar formula but account for storage costs and dividends․ These contracts allow hedging against price fluctuations, making them essential tools in risk management․ For detailed calculations and examples, refer to the futures pricing guide․

Budgeting and Cost Analysis

Budgeting involves creating financial plans to allocate resources efficiently․ Cost analysis evaluates expenses to optimize spending․ Key formulas include cost-benefit analysis and break-even analysis, essential for informed financial decision-making․

8․1․ Cost-Benefit Analysis Formula

The Cost-Benefit Analysis Formula evaluates project viability by comparing total benefits to total costs․ The formula is:
Benefit-Cost Ratio = (Total Benefits / Total Costs)․
When the ratio exceeds 1, the project is profitable․ This method helps prioritize investments and allocate resources efficiently․ Refer to the PDF guide for detailed examples and applications․

8․2․ Break-Even Analysis Formula

The Break-Even Analysis Formula calculates the point where total revenues equal total costs, ensuring no profit or loss․ The formula is:
BEP = Fixed Costs / (Selling Price ⏤ Variable Costs)․
This tool helps businesses determine the production volume or sales required to break even, enabling informed decisions on pricing and cost management․ For further details, refer to the PDF guide․

This section summarizes key financial mathematics formulas, emphasizing their practical applications in finance and investment decisions, as detailed in the PDF guide․

9․1․ Summary of Key Financial Mathematics Formulas

Financial mathematics involves essential formulas for calculating interest, present value, future value, annuities, and investment analysis․ Key formulas include simple interest, compound interest, net present value (NPV), internal rate of return (IRR), and the Capital Asset Pricing Model (CAPM)․ These tools help professionals make informed decisions․ The PDF guide provides comprehensive details on these formulas and their applications, ensuring a solid foundation in financial mathematics․

9․2․ Practical Applications of Financial Mathematics

Financial mathematics formulas are widely applied in real-world scenarios, such as calculating returns on investments, assessing project viability through NPV and IRR, and managing risk using the CAPM․ Professionals use these tools to evaluate loan payments, optimize investment portfolios, and determine the value of financial derivatives․ The practical applications extend to corporate finance, portfolio management, and risk assessment, making financial mathematics indispensable for informed decision-making․ The PDF guide provides detailed examples and calculations for these practical scenarios․