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Finance Lessons

Portfolio Theory

Final Exam: The Portfolio Theory Gauntlet

A graded, locked capstone exam across all of portfolio theory — diversification, correlation and covariance, portfolio risk and return, the efficient frontier, the Capital Market Line, and CAPM.

15 min Updated Jun 4, 2026

Training wheels off. The six lessons handed you the entire machine — why diversification is the one free lunch in finance, how correlation and covariance glue assets together, where a portfolio’s return and risk really come from, the efficient frontier that throws out every dominated portfolio, the Capital Market Line that a risk-free asset bends straight, and CAPM, which prices the only risk you can’t diversify away. Now the course asks whether it stuck. Read every option twice. The trap is almost always the one that sounds 90% right.

Warning:

How this exam works

This is a graded exam. Questions come one at a time. Once you submit an answer it is final — there is no going back, no second try, and a wrong answer simply fails that question. Your score stays hidden until the end, where you need 70% to pass. Read every option twice before you commit.

Question 1 of 27

Diversification reduces one kind of risk but is powerless against another. Which pair is correct?

Select an answer to continue.

Course Recap

Success:

If you cleared 70%, you can now reason about a portfolio the way a quant does: where return and risk come from, why correlation is the lever, which portfolios are worth holding, how a risk-free asset straightens the frontier into a single best line, and why the market only pays you for the risk you can’t diversify away. That’s the full arc of modern portfolio theory — from intuition to the equations practitioners actually use.

Big picture

Portfolio theory in one map

  • Modern portfolio theory, end to end
    • Why diversify
      • Idiosyncratic risk can be diversified; systematic cannot
      • Risk falls toward a floor: the market's systematic risk
      • The free lunch: less risk, same expected return
      • Correlations spike toward 1 in a crisis
    • Correlation & covariance
      • Covariance sign = direction of co-movement
      • Correlation lives in [−1, +1]
      • σ_p² = w_A²σ_A² + w_B²σ_B² + 2w_Aw_Bρσ_Aσ_B
      • ρ = −1 can cancel risk entirely; ρ = +1 cannot
    • Portfolio risk & return
      • E[R_p] = weighted average of returns
      • Risk < weighted average when ρ < 1
      • Minimum-variance portfolio = leftmost point
      • The bullet bends from diversification
    • Efficient frontier
      • Efficient = best return for its risk
      • Frontier runs upward from the MVP
      • Lower arm is dominated, excluded
      • Limitation: extreme sensitivity to estimation error
    • Capital Market Line
      • Risk-free asset → straight line
      • Touches frontier at the tangency / market portfolio
      • Slope = market Sharpe ratio
      • Two-fund separation; lending vs. borrowing (leverage)
    • CAPM
      • Beta = sensitivity to the market
      • Only systematic risk is priced
      • E[R_i] = r_f + β_i(E[R_M] − r_f)
      • Alpha = actual − CAPM; SML (β) vs CML (σ)
Six lessons, one picture: why diversification is the free lunch, how correlation and covariance bind assets, where portfolio risk and return come from, the efficient frontier that discards dominated mixes, the Capital Market Line a risk-free asset creates, and CAPM, which prices only systematic risk.

That’s portfolio theory, start to finish. Diversification, the covariance that powers it, the frontier of portfolios worth holding, the line a risk-free asset draws through them, and CAPM’s verdict that only undiversifiable risk earns a reward — you can now reason about each from first principles, which is exactly what it takes to build and judge a real portfolio.

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