Derivatives, Alternative Investments, Portfolio Management, and Ethical and Professional Standards E-Book

Azhar ul Haque Sario

• Herausgeber: Azhar Sario Hungary
• Kategorie: Fachliteratur
• Sprache: Englisch

Seitenzahl: 252

Veröffentlichungsjahr: 2025

Beschreibung

Ace the final subjects of your CFA Level 1 exam with this essential study guide!

This book is your focused guide to mastering four key areas of the CFA curriculum. We start with Derivatives. You will learn about derivative instruments and their markets. We explore forward commitments and contingent claims. You'll understand the benefits and risks of these tools. We cover the core concepts of arbitrage and replication. The book details the pricing and valuation of forwards, futures, swaps, and options. You will also learn about option replication using put–call parity and valuing derivatives with a binomial model. Next, we dive into Alternative Investments. This section introduces their unique features and structures. You'll learn how to analyze their performance and returns. We cover investments in private equity and debt. The guide explores real estate, infrastructure, and natural resources. It also provides a clear overview of hedge funds and an introduction to the world of digital assets. The third subject is Portfolio Management. Here, we break down portfolio risk and return in two detailed parts. You will get an overview of the entire portfolio management process. We teach the basics of portfolio planning and construction. You'll also explore the behavioral biases that affect individual investors and get a solid introduction to risk management. Finally, we cover Ethical and Professional Standards. This section explains the importance of ethics and trust in finance. It provides a thorough review of the Code of Ethics and Standards of Professional Conduct. You will find detailed guidance for all seven standards, an introduction to the Global Investment Performance Standards (GIPS), and practical ethics applications to solidify your understanding.

What makes this study aid different? We know you have dense textbooks and official materials. This book isn't designed to replace them; it's designed to make them easier to understand. We cut through the academic jargon and complex language. We present the core, examinable concepts in a clear, concise, and conversational way. Think of this as your expert study partner, simplifying difficult topics so you can learn more efficiently. While other books might overwhelm you with information, our guide focuses on reinforcing your knowledge and building your confidence for exam day. We get straight to the point, helping you connect the dots between different concepts and prepare for the kind of questions you'll actually face. It's the perfect tool for your final review, helping you solidify what you've learned and pinpoint any areas that need more attention.

Disclaimer: The author and this publication are not affiliated with, endorsed by, or sponsored by the CFA Institute. CFA Institute does not endorse, promote, or warrant the accuracy or quality of the products or services offered by the author. CFA® and Chartered Financial Analyst® are trademarks owned by the CFA Institute. This study aid is an independent product created for educational purposes under the principle of nominative fair use.

Leseprobe

Derivatives, Alternative Investments, Portfolio Management, and Ethical and Professional Standards: CFA Level 1 Study Aid

Azhar ul Haque Sario

Copyright

Copyright © 2025 by Azhar ul Haque Sario

All rights reserved. No part of this book may be reproduced in any manner whatsoever without written permission except in the case of brief quotations embodied in critical articles and reviews.

First Printing, 2025

[email protected]

ORCID: https://orcid.org/0009-0004-8629-830X

LinkedIn: https://www.linkedin.com/in/azharulhaquesario/

Disclaimer: This book is free from AI use. The cover was designed in Canva.

Disclaimer: The author and this publication are not affiliated with, endorsed by, or sponsored by the CFA Institute. CFA Institute does not endorse, promote, or warrant the accuracy or quality of the products or services offered by the author. CFA® and Chartered Financial Analyst® are trademarks owned by the CFA Institute. This study aid is an independent product created for educational purposes under the principle of nominative fair use.

Contents

Copyright

Subject 1: Derivatives

Derivative Instrument and Derivative Market Features

Forward Commitment and Contingent Claim Features and Instruments

Derivative Benefits, Risks, and Issuer and Investor Uses

Arbitrage, Replication, and the Cost of Carry in Pricing Derivatives

Pricing and Valuation of Forward Contracts and for an Underlying with Varying Maturities

Pricing and Valuation of Futures Contracts

Pricing and Valuation of Interest Rates and Other Swaps

Pricing and Valuation of Options

Option Replication Using Put–Call Parity

Valuing a Derivative Using a One-Period Binomial Model

Subject 2: Alternative Investments

Alternative Investment Features, Methods, and Structures

Alternative Investment Performance and Returns

Investments in Private Capital: Equity and Debt

Real Estate and Infrastructure

Natural Resources

Hedge Funds

Introduction to Digital Assets

Subject 3: Portfolio Management

Portfolio Risk and Return: Part I

Portfolio Risk and Return: Part II

Portfolio Management: An Overview

Basics of Portfolio Planning and Construction

The Behavioral Biases of Individuals

Introduction to Risk Management

Subject 4: Ethical and Professional Standards

Ethics and Trust in the Investment Profession

Code of Ethics and Standards of Professional Conduct

Guidance for Standards I–VII

Introduction to the Global Investment Performance Standards (GIPS)

Ethics Application

About Author

Subject 1: Derivatives

Derivative Instrument and Derivative Market Features

Of Shadows and Echoes: A Creative Look at Derivatives

Imagine standing in a vast canyon. You shout, and a moment later, your voice returns to you, changed by the distance and the rock—an echo. It isn't your original voice, but it owes its entire existence to it. This is the heart of a financial derivative. It’s a financial echo, a contract whose value is a shadow of something real and tangible—a stock, a barrel of oil, a bundle of currency, or even the weather. You don't own the mountain, but you can trade its shadow, betting on how it will stretch and shrink as the sun moves across the sky.

The Magic and Mayhem of Financial Echoes

These aren't just simple contracts; they are powered by some incredible, and sometimes dangerous, forces.

First, they offer leverage, which is like a financial crowbar. With a small push of your own capital, you can move a massive weight. It’s the magic that allows a modest investment to control a fortune in assets. If the market moves your way, the crowbar lifts your profits to exhilarating heights. But if it moves against you, that same crowbar can bring the entire weight crashing down, turning a small mistake into a catastrophic loss. It's the financial equivalent of riding a tiger—thrilling, but you can’t afford to fall off.

So why ride the tiger? Often, it’s for protection. This is called hedging, and it’s like building a financial umbrella before it starts to rain. Think of an airline. The price of jet fuel is a wild, bucking bronco that can trample their profits overnight. Using a derivative, they can lock in a future price, taming that bronco into a steady, predictable trot. It's a tool for transforming crippling uncertainty into manageable risk, allowing businesses to focus on what they do best, rather than gambling on the whims of the market.

Of course, some people love the thrill of the gamble. This is speculation. Speculators are the market’s fortune tellers, using derivatives as their crystal ball. They don't want to tame the bronco; they want to bet on which way it will jump. If you have a powerful hunch that a tech company's stock is about to soar, you can buy a derivative that acts like a golden ticket—the right to buy that stock later at today's price. If you’re right, your ticket becomes incredibly valuable. It’s a high-stakes game of foresight, where fortunes can be made and lost on a vision of tomorrow.

Finally, these instruments are not forever. Unlike a share of stock you can tuck away for a lifetime, a derivative is a financial sandcastle. It's built with specific terms and a ticking clock—an expiry date. When the tide of time comes in, the contract is settled, and the sandcastle washes away, leaving behind either a treasure of profit or the debris of a loss.

The Two Worlds of Derivatives: A Tale of Two Markets

These financial echoes don't all live in the same place. They inhabit two very different universes: the bespoke, private world of the Over-the-Counter market and the bustling, public square of the Exchange-Traded market.

1. The Over-the-Counter (OTC) Market: The Secret Handshake

Imagine a world of finance that operates like a bespoke tailor shop. This is the OTC market. There’s no central building or screaming trading floor. It’s a decentralized network of institutions making private deals, crafting contracts from scratch to fit a client’s exact needs. An agreement is made with a direct, digital handshake between two parties.

The beauty here is customization. Need to hedge against the price of a rare earth metal for exactly 37 months? The OTC market can build that for you. But this bespoke world has its own ghost in the machine: counterparty risk. You’re trusting the person on the other side of your handshake to make good on their promise. What if they go broke? Your perfectly tailored contract could vanish into thin air. It’s a world built on trust and credit checks, where the shadows are long and the dealings are quiet. The prices are whispered, not shouted, and trying to sell your custom-made contract to someone else can be like trying to sell a suit tailored perfectly for another person—nearly impossible.

2. The Exchange-Traded Market: Grand Central Station

Now, picture the opposite: a brightly lit, public marketplace, buzzing with energy, with prices flashing on giant screens for all to see. This is the world of the exchange. Think of it as the Grand Central Station of derivatives.

The defining feature here is standardization. The contracts are like items on a global fast-food menu; an option to buy 100 shares of Apple is the same whether you’re in Chicago or Frankfurt. This "cookie-cutter" approach means they are incredibly easy to buy and sell, creating a deep, flowing river of liquidity.

Most importantly, this market has an ultimate bodyguard: the clearinghouse. This institution stands between every single buyer and seller, acting as an unflappable middleman. It guarantees every single trade. Your deal is with the clearinghouse, not the person on the other end. This eliminates the fear of your counterparty ghosting you, making the market incredibly safe and stable. It’s a world of transparency, trust, and perpetual motion.

In the end, the secretive OTC market and the open exchange are two sides of the same coin. One offers limitless flexibility for those with unique needs and the muscle to manage the risk. The other offers safety, simplicity, and speed for the masses. Together, they create a dynamic landscape where risk can be sculpted, bets can be placed, and the echoes of the real economy can be traded in a mesmerizing, high-stakes dance.

Forward Commitment and Contingent Claim Features and Instruments

Navigating the Future: A Guide to Financial Derivatives

The future is an uncharted sea. It’s a realm of maybes, what-ifs, and unknowns. For centuries, we’ve built tools to navigate uncertainty, and in the world of finance, these tools are called derivatives. They aren’t tangible assets you can hold in your hand, like a stock certificate or a gold bar. Instead, they are contracts, promises, and possibilities—ghosts of value whose worth is derived from something real and tangible.

Think of them as different ways to negotiate with tomorrow. Some are ironclad promises, while others are flexible "maybe" clauses. Let's meet the cast of characters.

1. The Cast of Characters: A Field Guide to Derivatives

The Handshake Deal: Forward Contracts

Imagine you're an artisan baker famous for your sourdough, and a local farmer grows the specific organic wheat you need. You're worried the price of wheat will skyrocket before your next big order in three months. The farmer is worried the price might plummet. So, you meet for coffee. You shake hands on a deal to buy a specific amount of his wheat, in three months, at a price you both agree on today.

That’s a forward contract. It’s a deeply personal, bespoke agreement.

The Vibe: Private, customized, and built on trust. You two decide everything—the exact quality of the wheat, the price, the delivery date.

The Room: It happens "Over-the-Counter" (OTC), which is just a fancy way of saying you do it directly, without a formal exchange or a middleman.

The Risk: What if the farmer gets a better offer and ghosts you? Or what if your bakery has a slow season and you can't afford the wheat? This is counterparty risk—the risk that the other person won't hold up their end of the bargain. It’s the major vulnerability of a private handshake.

The Public Vow: Futures Contracts

Now, imagine that same deal, but instead of a private handshake, you make your vow in the middle of a bustling town square. This is a futures contract. It’s a forward contract that has been standardized and brought out into the open for everyone to see and trade.

The Vibe: Standardized, transparent, and public. The contracts are like Lego bricks—every piece (quantity, quality, date) is a standard size, so they can be easily traded between strangers.

The Room: It happens on an organized exchange, a financial town square like the Chicago Mercantile Exchange (CME).

The Guardian: The exchange has a clearinghouse, which acts like a trusted town elder. It stands between every buyer and seller, guaranteeing that no one can back out of their promise. This almost entirely eliminates counterparty risk. To ensure this, the clearinghouse performs a daily ritual called "marking-to-market," where it settles all gains and losses every single day. If your bet goes sour, you pay up immediately, not just at the end.

The Great Exchange: Swaps

A swap is less like a single promise and more like an ongoing relationship. Imagine you have a variable-rate mortgage, and the anxiety of fluctuating payments keeps you up at night. Your friend has a predictable fixed-rate mortgage but is an adrenaline junkie who believes rates are about to plummet and wants in on the action.

A swap lets you trade situations. You agree to pay her fixed-rate payment, and she agrees to pay your variable-rate payment. You don't trade houses; you just swap the financial headaches.

The Vibe: A long-term exchange of cash flows. The most common is an interest rate swap, but people also swap currencies or commodity payments.

The Foundation: The payments are calculated based on a "notional principal"—a hypothetical amount of money that's used for the math but never actually changes hands. It's the "what if" number that powers the whole deal.

The Room: Like forwards, swaps are often customized OTC deals, making them flexible but also carrying counterparty risk.

The 'Maybe' Clause: Options (Calls and Puts)

Options are the most fascinating of the bunch. They give you the right, but not the obligation, to do something. You are essentially buying a choice. To get this power, you pay a small, non-refundable fee called a premium.

Call Options: The Right to Buy. You'd buy a call if you believe the price of an asset is going to the moon. It's like paying a small fee to reserve a hot concert ticket at today's price. If the band blows up and ticket prices skyrocket, you can exercise your right and buy it cheap. If the band is a flop, you just let your reservation expire. You only lose the reservation fee (the premium).

Put Options: The Right to Sell. You'd buy a put if you fear the price of an asset is about to crash. It’s like buying insurance on your car. If you get in a wreck (the price crashes), the insurance pays out. If you drive safely (the price stays high), you don't use the insurance. You're just out the cost of your premium.

Options can be American (you can exercise your right anytime before it expires) or European (you can only exercise on the final expiration day).

The Insurance Policy on a Promise: Credit Derivatives

Imagine a bank has lent a billion dollars to a risky startup. The bank is proud of the deal but also has nightmares about the startup going bankrupt. A credit derivative lets the bank offload that specific nightmare.

The most common type is a Credit Default Swap (CDS). The bank (the protection buyer) pays a regular fee, like an insurance premium, to another investor (the protection seller). If the startup defaults on its loan (a "credit event"), the investor pays the bank a large sum to cover its losses.

The Vibe: It's a side-bet on survival. You're not trading the loan itself, but the risk of that loan going bad. It's how you can hedge against default or, more controversially, speculate on a company's or even a country's potential financial collapse.

2. Cashing In Your 'Maybe' Ticket: Option Profits at Expiration

Let's demystify how you make or lose money with options. It all comes down to the face-off between the Strike Price (K)—the price locked into your option—and the Spot Price (ST)—the actual market price when the option expires.

The Bullish Bet: A Long Call Option

You buy a call option, betting the price will rise.

Value at Expiration: The option's value is the better of two worlds: either the profit you'd make by using it, or zero. You'd never use it to lose money. So, its value is $max(0, S_T - K)$.

Your Profit: Your actual profit is that value, minus the premium you paid to get the ticket in the first place.

The Bottom Line: Your loss is capped at the premium you paid. Your potential profit is, theoretically, infinite.

The Bearish Bet: A Long Put Option

You buy a put option, betting the price will fall.

Value at Expiration: The option's value is the profit from selling at the high strike price after buying at the low market price, or zero. So, its value is $max(0, K - S_T)$.

Your Profit: Again, it's the option's value minus what you paid for it.

The Bottom Line: Your loss is capped at the premium. Your maximum profit is capped at the strike price (since the asset's price can't fall below zero).

Selling an Option (The Short Position)

When you sell (or "write") an option, you are the one collecting the premium. You are taking the other side of the bet.

Short Call Seller: You hope the price stays flat or falls. Your profit is capped at the premium you received, but your potential loss is unlimited. You have all the risk for a small reward.

Short Put Seller: You hope the price stays flat or rises. Your profit is capped at the premium, and your potential loss can be very large (down to the strike price).

3. Ironclad Promises vs. Strategic Maybes

The deepest divide in the world of derivatives is the nature of the promise itself.

Forward Commitments: The Ironclad Promise

These are instruments where both parties are locked in. You have an obligation to perform, no matter what. There’s no backing out. The deal will happen, for better or for worse. The risk and reward are typically symmetric—one person's gain is the other's loss.

The Roster: Forward Contracts, Futures Contracts, Swaps.

The Price of Entry: Usually zero upfront. You're committing your future self, not your present cash.

The DNA: A two-way obligation. A binding pact.

Contingent Claims: The Strategic Maybe

These are instruments where one party buys a right, and the other sells an obligation. The buyer pays a premium for the flexibility to walk away. The seller collects that premium in exchange for being on the hook if the buyer decides to act.

The Roster: Options (Calls and Puts), Credit Derivatives.

The Price of Entry: The buyer must pay a premium to acquire the choice.

The DNA: A one-way obligation. The risk and reward are asymmetric—the buyer has limited risk and high potential reward, while the seller has limited reward and high potential risk.

In essence, forward commitments are about saying, "We WILL do this." Contingent claims are about paying for the right to say, "I MIGHT do this, and you have to let me." Understanding this single difference is the key to unlocking the entire landscape of modern finance.

Derivative Benefits, Risks, and Issuer and Investor Uses

Step into the world of finance, and you'll find a hidden, parallel universe. It’s not a market of things you can touch, like gold bars or company stocks, but a market of ghosts. These are the ghosts of tomorrow’s prices, the echoes of future events, the shimmering shapes of what might be. This ethereal marketplace is the world of derivatives.

These financial instruments aren’t assets themselves; they are contracts, bets, and promises based on the future behavior of something real—a stock, a currency, a barrel of oil. They are financial alchemy, tools of immense power that can forge fortunes or unleash ruin. To understand them is to understand the art of dancing with shadows.

The Two Faces of the Shadow: Promise and Peril

Like any powerful magic, derivatives offer both salvation and seduction. Their nature is a paradox, a tightrope walk between security and speculation.

The Allure: Mastering the Future's Ghost

At its heart, the magic of derivatives is about taming uncertainty. Imagine you're a craft chocolate maker, and your entire business depends on rare cacao beans from a single region prone to political instability. The fear of a sudden price spike keeps you up at night. Using a derivative, you can cast a spell—a "futures contract"—that locks in the price of your beans six months from now. You’ve captured the ghost of that future price and made it solid. The anxiety vanishes. You’re no longer a victim of the market's whims; you’re its architect, free to focus on the art of making chocolate. This is hedging: building a shield against a chaotic future.

Then there's the intoxicating allure of leverage, the art of whispering to a giant. With an "option," you don't need the immense capital to buy a thousand shares of a tech company. You can buy the right to purchase them. With a sliver of the cost, you control the potential of the whole block. If the stock soars, your small whisper becomes a deafening roar of profit. It’s the financial equivalent of using a tiny key to turn the engine of a massive machine, offering amplified returns to those who can master its mechanics.

This constant trading of promises and possibilities—the collective dream of the market—also creates a kind of crystal ball. The price of a derivative is a living prophecy, a consensus forecast of where the world is heading. This “price discovery” makes the real markets smarter, more transparent, and more efficient for everyone.

The Betrayal: When the Shadows Turn on You

But shadows can be treacherous. The same leverage that magnifies your gains can become a devastating undertow. The giant you were whispering to can stumble, and when it falls, it can crush you. A small, unfavorable tick in the market can vaporize your initial investment and leave you owing vastly more. It’s a fire that can warm your hands or burn your house down.

The complexity of these instruments is another danger. They are not simple tools; they are intricate spellbooks written in a language of arcane mathematics and legal jargon. To misunderstand a single clause, to misinterpret one variable in the incantation, is to risk the spell backfiring with catastrophic consequences. Many a fortune has been lost not to a bad bet, but to a poorly understood one.

And what happens when the other side of your magical pact simply vanishes? In the vast, less-regulated spaces of the derivative world, you face “counterparty risk”—the chilling possibility that the person or institution that promised to pay you simply won’t. They default, they disappear, and your perfectly crafted shield turns to dust in your hands. It’s the ultimate betrayal: a broken promise in the ghost market.

The Shadow Weavers: The Architects and the Fortune Tellers

People come to this shadow market for vastly different reasons. They fall into two main camps: those looking to build walls and those looking to find treasure.

The Architects: Building for Certainty

On one side are the issuers: the corporations, the airlines, the governments. These are the builders of the tangible world. They aren't in the market for thrills; they are there for stability. An airline, whose lifeblood is jet fuel, doesn't want to gamble on the price of oil. They enter the shadow market to build financial scaffolding around their business, using derivatives to neutralize the wild swings in fuel costs. A multinational company building a factory in Europe uses derivatives to transform the shifting sands of the Euro/Dollar exchange rate into solid ground.

For them, derivatives are defensive tools. They are the ballast that keeps the ship steady, the shock absorbers that smooth out a bumpy economic road. Their goal is not to win the game, but to ensure they can finish building what they started, regardless of the storms raging outside.

The Fortune Tellers: Dancing with Chance

On the other side are the investors: the hedge funds, the traders, the sophisticated speculators. They are the adventurers, the seers, the shadow dancers. They don't have a factory to protect; their business is the storm. They come to the shadow market to read the tea leaves, to predict the weather, and to place their bets accordingly.

They use derivatives as their divining rods and crystal balls. Believing a stock is undervalued, they won’t just buy the stock; they will buy call options, hoping to ride the wave of its ascent for a fraction of the cost. Sensing a downturn, they’ll use derivatives to short the market, profiting from the fall. Some even develop elegant strategies to generate income, like selling “covered calls,” a process akin to renting out the ghost of a stock they already own for a steady premium.

For this tribe, derivatives are offensive weapons and tools of exploration. They seek to harness volatility, to dance with risk and lead it to a profitable conclusion. They live and breathe in the shadow market, their fortunes rising and falling with its ethereal tides.

In the end, the world of derivatives is a mirror. It reflects our deepest financial desires—our fear of the unknown and our hunger for gain. It is neither good nor evil, but it is undeniably powerful. It’s a world of ghosts we’ve created, and learning to see them clearly is the only way to avoid being haunted by them.

Arbitrage, Replication, and the Cost of Carry in Pricing Derivatives

The Magician's Secret and the Time-Traveling Asset

Modern finance often feels like a magic show. Derivatives, with their exotic names and dizzying complexity, seem like the grandest illusions of all. But behind every great magic trick, there's a simple, elegant secret. In finance, that secret rests on two beautifully human ideas: you can’t be in two places at once, and you can't build something for $10 and sell it for $50 if everyone knows the recipe.

These are the bedrock principles of arbitrage and replication.

Deconstructing the Magic: Replication and the Skeptical Audience

Imagine a master financial magician on a stage. He presents a "Call Option"—a wondrous ticket that gives you the right to buy a popular stock at a fixed price a year from now. How much should you pay for this magical ticket? It seems impossible to know. Its value depends on the future, which is a closed book.

Instead of trying to guess, we pull back the curtain. This is replication. We realize we don’t need the magician’s specific trick. We can recreate the exact same outcome ourselves using things we can buy right now. Think of it like a financial recipe. We can build our own version of that "magical ticket" using a precise mixture of two simple ingredients: a portion of the underlying stock itself and a loan from a bank (or a risk-free bond).

The fundamental law of finance is this: the price of the magic trick can never be more than the cost of its ingredients. If the magician tries to sell his option for $10, but we can build our own replicating portfolio for just $8, an enormous, flashing neon sign of opportunity appears.

This is where the second concept, arbitrage, enters the theater. Arbitrage is the skeptic in the front row who knows how the trick is done. The moment the magician overprices his trick, the arbitrageur leaps into action. They'll sell the magician's expensive $10 ticket and simultaneously build the identical $8 version themselves, instantly pocketing $2 of pure, risk-free profit.

This arbitrageur isn't just one person; it's the entire market, a collective intelligence that acts as a powerful enforcer. They are the hecklers who keep the magicians honest. Their relentless pursuit of these "free lunches" forces the price of the derivative—the magic trick—to snap back to the cost of its replicating parts. Together, replication (the recipe) and arbitrage (the enforcer) ensure that even the most complex financial products have a fair, logical price rooted in the value of their simpler components.

The Price of Time: Spot vs. Future and the Cost of a Journey

Now, let's look at the ingredients themselves—the assets that underpin everything. We often talk about an asset's price, but it has two identities: its price today and its price tomorrow.

The spot price is the asset's price in the here and now. It’s the cost of a barrel of oil if you want it rolled onto your dock this afternoon. It’s the price of a share of stock that lands in your account instantly. It is reality, right now.

The future price is different. It isn't a prediction or a guess; it's a reservation. It's the price you agree upon today to have that same asset delivered to you at a specific point in the future.

So why would these two prices be different? Because getting an asset from today to the future isn’t free. It has to go on a journey through time, and that journey has a cost. This is the cost of carry.

Think of it as the price of a time-travel ticket for your asset. What's included in the fare?

The Baggage Fee (Storage & Insurance): If you're sending a physical commodity like gold or grain into the future, you can't just wish it there. You have to pay to store it in a secure vault or a dry silo. You have to insure it against theft or spoilage. These are the direct costs of its journey.

The Price of the Ticket (Financing): To buy that asset today, you had to use capital. That capital could have been sitting in a bank, happily earning interest. The interest you're not earning because your money is tied up in the asset is a very real cost. It’s the opportunity cost, the price of admission for the journey.

The In-Flight Perks (Yields & Dividends): Sometimes, the asset pays you back during its trip! A stock might issue a dividend, like a complimentary meal service. A physical commodity might offer a "convenience yield"—a hidden benefit of having it on hand, ready for your factory to use. This is crucial for businesses that can't afford to halt production while waiting for a shipment. These perks reduce the net cost of the time-travel ticket.

The fair future price is simply today's spot price plus the net cost of this time-travel ticket. The famous cost of carry model is just the formal travel itinerary:

F=S×e(r+Storage−Yield)×T

This equation just says: The Future Price (F) equals the Spot Price (S) plus all the costs of its journey through time (T), minus any perks it gives you along the way.

And just like with our magic trick, if the futures market (the time-travel agency) tries to charge a price different from this calculated cost, the arbitrageurs step in. They'll buy the asset in one time zone (the present) and sell it in another (the future) to pocket the difference, instantly correcting the market's pricing.

Ultimately, from the most elaborate derivative to the simplest commodity, the market is governed by this beautiful, grounded logic. Prices are not abstract guesses; they are tethered to the real-world costs of creating, holding, and moving assets through time. The magic, it turns out, is no magic at all. It's just a matter of knowing the recipe and the price of the ticket.

Pricing and Valuation of Forward Contracts and for an Underlying with Varying Maturities

1. The Promise and the Phantom: A Forward Contract's Journey

Imagine making a handshake deal with a friend—a promise sealed across time. You agree, right now, to buy their vintage bicycle in six months for a fixed price of $400. This is the soul of a forward contract: a simple promise between two people, custom-built for a specific need, far from the clamor of a public exchange. It’s a financial instrument at its most personal.

But this promise has a curious dual nature. It has a price, and it has a value, and they are two very different beasts that live a fascinating life together.

The Moment of Creation: A Perfectly Balanced Start

When you and your friend first shake hands on the deal, the contract itself is like a perfectly balanced scale. The price is set in stone: $400. That number will never change. It's the anchor for your entire agreement.

But what is the contract’s value at this moment? Zero. Nothing. A weightless agreement. This feels strange, doesn't it? You've just committed to a future transaction, yet it has no immediate worth.

Here’s why: that $400 price wasn't picked from a hat. It was carefully chosen to be the market's best, fairest guess of what that bicycle will be worth in six months. It’s the equilibrium point where neither you nor your friend has an edge. You’re happy to lock in the price, and they're happy to lock in a sale. No money changes hands. It's a clean start, a zero-sum game where the potential for future profit or loss is coiled up, waiting for time to pass. The price is set precisely to prevent anyone from having an instant, risk-free win. The stage is set, but the play hasn't started.

The Passage of Time: The Phantom Value Awakens

A month goes by. The fixed $400 price of your contract is still your anchor, unchanging. But the world outside has shifted. A famous cyclist wins a major race on a similar vintage bike, and suddenly, they're all the rage. The estimated future market price for your friend's bike is now closer to $500.