Investments 101
A compressed tour of my undergraduate finance education, from time value of money through portfolio optimization. Each post contains interactive tools to explore the math.
12 posts
- 1
Financial Markets & Securities
What financial assets are, how markets work, and why the bid-ask spread is the price of immediacy.
- 2
The Time Value of Money
Why a dollar today beats a dollar tomorrow, and how compound interest turns a small return into a large balance.
- 3
Bond Pricing & Yield
How to price a bond from first principles, why prices and yields move in opposite directions, and what the shape of the yield curve is trying to say.
- 4
Duration & Convexity
Macaulay duration, modified duration, and convexity: the math behind how sensitive a bond's price is to interest rate changes.
- 5
Stocks & Valuation
The dividend discount model, multi-stage growth, implied returns, P/E ratios, and why small input changes produce big price swings.
- 6
Risk & Return
Expected return, variance, standard deviation, the normal model, Value at Risk, the Sharpe ratio, and why measuring risk is harder than measuring return.
- 7
Portfolio Returns
Portfolio weights, the weighted-average return formula, buying on margin, short selling, leverage, rebalancing, and how the major stock indexes are built.
- 8
Diversification & Portfolio Risk
Covariance, correlation, the two-asset portfolio variance formula, the diversification curve, systematic vs. idiosyncratic risk, and why diversification is the closest thing to a free lunch in finance.
- 9
Capital Allocation & the Efficient Frontier
Why volatility is costly, the Capital Allocation Line, the Sharpe ratio as the slope of the CAL, Two Fund Separation, scaling vs. tilting, the efficient frontier, and the tangent portfolio.
- 10
CAPM & Factor Models
From tangent portfolio to market portfolio, why diversifiable risk earns no premium, beta, the CAPM and Security Market Line, alpha, multi-factor models (Fama-French), and arbitrage pricing theory.
- 11
Portfolio Optimization
The covariance matrix for N assets, why covariances dominate portfolio risk, alpha as a gradient for improving the Sharpe ratio, tilting toward positive alpha, and the CAPM as an optimality condition.
- 12
Market Efficiency
The efficient market hypothesis, its three forms, the evidence for and against it, the Grossman-Stiglitz paradox, and what it all means for investors.