Introduction to ROI: CAPM, APT Models & Financial Derivatives

Modern financial management has evolved far beyond traditional bookkeeping. In globalized financial markets, corporate treasurers must understand how asset prices are determined in relation to risk and how to protect corporate profits against price volatility using Financial Derivatives.

1. What is Return on Investment (ROI)?

Return on Investment (ROI) is the universal performance measure used to evaluate the efficiency and profitability of an investment or to compare the efficiency of several different investments:

ROI = (Net Financial Return / Total Cost of Investment) × 100

In corporate financial strategy, the critical question is: What rate of return should investors legitimately demand for bearing risk? This led to the development of modern asset pricing models.

2. Capital Asset Pricing Model (CAPM)

Developed by Nobel Laureate William Sharpe (building on Harry Markowitz’s Modern Portfolio Theory), CAPM establishes the direct linear relationship between the required return on a security and its systematic risk (Beta).

Fundamental Premise:

In a diversified portfolio, unsystematic (company-specific) risk is eliminated. Therefore, investors should only be rewarded for bearing Systematic (Market) Risk, which cannot be diversified away.

The CAPM Formula:

Expected Return [E(R)] = Rf + β × (Rm - Rf)

Where:

Rf (Risk-Free Rate): The return on a default-free government security (e.g., 91-day Government of India Treasury Bills yielding 6.5%).
β (Beta Coefficient): The measure of the asset’s systematic risk relative to the overall market index (Nifty 50 or Sensex).
Rm: The expected average return on the broad market portfolio (e.g., historical Nifty return of 13%).
(Rm - Rf): The Market Risk Premium (the extra return demanded by investors for switching from risk-free government bonds into risky equities).

Solved Practical Numerical Problem on CAPM:

Risk-Free Rate of Return (Rf): 7.0%
Expected Return on the Market Index (Rm): 14.0%
Stock Beta (β): 1.25

Step-by-Step Calculation:

Market Risk Premium = Rm - Rf = 14.0% - 7.0% = 7.0%
Risk Premium for the Stock = β × (Rm - Rf) = 1.25 × 7.0% = 8.75%
Required Rate of Return:

Expected Return = 7.0% + 8.75% = 15.75%

Managerial Insight: An investor purchasing this stock should demand at least a 15.75% return to justify its above-average market risk (Beta = 1.25).

3. Arbitrage Pricing Theory (APT)

Developed by economist Stephen Ross in 1976, Arbitrage Pricing Theory (APT) was formulated as a more realistic multi-factor alternative to CAPM.

CAPM vs APT:

CAPM is a single-factor model: It assumes stock returns depend on only ONE macro factor: movement of the market index.
APT is a multi-factor model: It recognizes that several distinct macro-economic forces simultaneously influence a company’s stock price.

Macro-Economic Factors in APT:

Unanticipated changes in Inflation
Shifts in Industrial Production / GDP Growth
Fluctuations in the Term Structure of Interest Rates (Yield Curve)
Changes in Foreign Exchange Rates (Rupee vs US Dollar)
Changes in Global Crude Oil Prices

The APT Equation:

Expected Return = Rf + β1 × (Risk Premium 1) + β2 × (Risk Premium 2) + … + βn × (Risk Premium n)

Where each β measures the stock’s sensitivity to that specific macro-economic risk factor.

4. Introduction to Financial Derivatives

A Derivative is a financial contract whose value is derived from the value of an underlying asset (such as equity shares, stock market indices, currencies like the US Dollar, or commodities like crude oil and gold).

Why do Businesses Use Derivatives?

Hedging (Risk Reduction): A textile exporter in Indore who will receive 1,00,000 US Dollars in 3 months enters a forward contract to lock in the exchange rate today, completely eliminating currency risk!
Speculation: Traders taking market positions to make profits from anticipated price movements.
Arbitrage: Exploiting temporary price differences of the same asset in two different markets.

5. Major Types of Financial Derivatives

                       ┌───────────────────────────────┐
                       │     FINANCIAL DERIVATIVES     │
                       └───────────────┬───────────────┘
                                       │
     ┌───────────────────┬─────────────┴─────┬───────────────────┐
     ▼                   ▼                   ▼                   ▼
┌──────────────┐  ┌──────────────┐    ┌──────────────┐    ┌──────────────┐
│   FORWARD    │  │   FUTURES    │    │   OPTIONS    │    │    SWAPS     │
│  CONTRACTS   │  │  CONTRACTS   │    │(CALL & PUT)  │    │  CONTRACTS   │
└──────────────┘  └──────────────┘    └──────────────┘    └──────────────┘

A. Forward Contracts

A customized, private, over-the-counter (OTC) agreement between two parties to buy or sell an underlying asset at a specified price on a future date.
Not traded on formal exchanges; exposed to counterparty default risk.

B. Futures Contracts

A standardized, exchange-traded contract (traded on NSE or BSE) to buy or sell an asset at a predetermined price on a future delivery date.
Cleared and guaranteed by the exchange clearing corporation; zero counterparty default risk; requires daily mark-to-market margin.

C. Options Contracts (Call & Put)

A contract that gives the buyer the right, but not the obligation, to buy or sell the underlying asset:

Call Option: Gives the holder the right to BUY an asset at a predetermined strike price. (Used when expecting prices to rise).
Put Option: Gives the holder the right to SELL an asset at a predetermined strike price. (Used as insurance when expecting prices to fall).

Option Premium: The non-refundable fee paid upfront by the option buyer to the option seller (writer).

D. Swaps

A contractual agreement between two parties to exchange financial cash flows over a designated period (e.g., an Interest Rate Swap where a firm exchanges floating-rate bank interest for a fixed interest rate).

6. Summary & Quick Revision Checklist

CAPM Formula: Expected Return = Rf + β × (Rm - Rf); prices risk based solely on systematic Beta.
APT: Multi-factor asset pricing model incorporating inflation, GDP, interest rates, and foreign exchange.
Derivatives: Financial instruments whose value is derived from an underlying asset (equities, currencies, commodities).
Core Derivative Types: Forwards (customized OTC), Futures (standardized exchange-traded), Options (right without obligation: Call to buy, Put to sell), and Swaps (cash flow exchanges).
Primary Corporate Purpose: Hedging against business and financial risks.