Sukrit Mittal Franklin Templeton Investments
Where we’ve been, and why it matters for what comes next.
We have built a toolkit – layer by layer – for understanding how financial markets work mathematically.
| Block | Lectures | Core question |
|---|---|---|
| Foundations | 1–4 | How do we model markets and the value of money? |
| Portfolio Theory | 5–8 | How should an investor allocate capital? |
| Risk Measurement | 9–10 | How do we quantify and manage risk? |
| Derivatives | 11 | How do we price contracts whose value derives from other assets? |
Each block answers a question that the next block depends on.
What is a financial market, mathematically? Defined the objects of study: assets, prices, time, uncertainty. Established that finance is not storytelling – it is structure and abstraction.
What is the simplest non-trivial market? The one-step binomial model. Two states, one period – yet rich enough to introduce no-arbitrage, the single most important principle in all of mathematical finance.
Why is $1 today worth more than $1 tomorrow? Opportunity cost, inflation, risk. Moved from simple to compound to continuous compounding – the language derivatives pricing speaks in.
How do we price time itself? Bonds, discount factors, term structure. The yield curve encodes the market’s collective view of the future cost of money.
How do risk and return trade off? Defined return (simple, log), variance as risk, and the fundamental insight: you cannot earn more without accepting more risk – but you can be smart about which risks you take.
What happens when you can lend and borrow at a risk-free rate? The Capital Allocation Line: every efficient portfolio is a mix of the risk-free asset and one optimal risky portfolio. Introduced constrained optimization via Lagrange multipliers.
How does diversification work with many assets? Matrix/vector formulation. The efficient frontier as a hyperbola. Diversification doesn’t just reduce risk – it reshapes the entire opportunity set.
How are assets priced in equilibrium? If all investors optimize, the market portfolio is the optimal risky portfolio. An asset’s expected return depends only on its systematic risk (beta), not its total risk.
Why do different investors hold different portfolios? Expected utility theory formalizes risk aversion. Utility functions encode preferences; concavity measures how much an investor dislikes uncertainty. This is the theoretical backbone behind mean-variance analysis.
How bad can it get? VaR asks: “What is my maximum loss at a given confidence level?” Three methods – parametric, historical simulation, Monte Carlo. Powerful but limited: VaR says nothing about how bad losses can be beyond the threshold.
How do you lock in a price today for a transaction tomorrow?
Forward contracts: symmetric obligations. Priced by no-arbitrage replication – construct a portfolio that exactly mimics the payoff, and the price follows. Futures add daily margining to manage counterparty risk.
Key insight: the forward price is not a forecast. It is the unique price that prevents free money.
| Lecture | The one thing to remember |
|---|---|
| 1. Financial Systems | Finance = mathematical structure, not intuition |
| 2. Simple Market Model | No-arbitrage – the anchor of all pricing |
| 3. Time Value of Money | Continuous compounding as the natural language |
| 4. Money Market | The yield curve prices time |
| 5. Intro to Portfolios | Risk-return is a trade-off, not a choice |
| 6. Risk-Free + Optimization | One optimal risky portfolio for everyone |
| 7. Multi-Asset Portfolios | Diversification reshapes opportunity |
| 8. CAPM | Only systematic risk is rewarded |
| 9. Utility Functions | Preferences explain behaviour |
| 10. Value at Risk | Quantify downside, but respect its limits |
| 11. Forwards & Futures | Price by replication, not prediction |
\[ \boxed{\text{Model a market}} \;\longrightarrow\; \boxed{\text{Price time (bonds)}} \;\longrightarrow\; \boxed{\text{Combine assets (portfolios)}} \]
\[ \longrightarrow\; \boxed{\text{Quantify risk (utility, VaR)}} \;\longrightarrow\; \boxed{\text{Price derivatives (forwards)}} \]
Every step rests on one principle: no-arbitrage.
What if we want a contract that gives us the right, but not the obligation, to trade?
A forward contract is a symmetric bet: both sides are equally exposed.
But what if you could keep the upside and cut off the downside?
That is an option – and its asymmetric payoff changes everything:
No-arbitrage still rules – but the arguments become richer.