Risk, Return & the Equity Risk Premium

Learning objectives

By the end you can:

1. Compute expected return, variance, and standard deviation from a scenario table or a return history, and explain in plain words what σ measures, why it is built from squared deviations, and where its "±1σ about two-thirds of the time" reading breaks down.
2. Run two-asset portfolio arithmetic cold (expected return as the weighted average, portfolio σ from the full formula at any correlation, the minimum-variance weights) and state precisely why portfolio risk is less than the average of risks whenever correlation is below +1.
3. Explain systematic vs idiosyncratic risk with the n-stock variance floor, and reproduce the argument for why markets pay a premium only for the risk diversification cannot remove.
4. Sketch the Markowitz efficient frontier from a numeric example (no matrix algebra), add the risk-free asset, and explain how two-fund separation leads to the market portfolio.
5. Derive CAPM's logic intuitively (beta as covariance with the market divided by market variance, Re = Rf + β × ERP), compute a beta by hand from a small return table, and give a fair, two-sided account of CAPM's empirical record (flat SML, Fama-French, unstable betas, Roll's critique) and why practitioners still use it.
6. Estimate the equity risk premium three ways: survey, historical (arithmetic vs geometric, standard error, survivorship, and why India's own history is nearly unusable), and implied (solve the market's IRR from index level and expected cash flows, Damodaran's method). State each estimate's failure modes.
7. Build a country risk premium for India with Damodaran's method (sovereign default spread × relative equity volatility), apply it with revenue-weighting (λ) so exporters and domestic businesses get different premiums, and avoid the double-counting trap with the risk-free rate.
8. Pull every live input from its named source: Damodaran's implied-ERP and country-risk pages, FRED for US Treasury yields, RBI/CCIL for G-sec yields. Maintain a dated "ERP card" in your knowledge system, refreshed every January.

Prerequisites & connections

Builds on. M0.03 (the rate stack: waiting + inflation + doubt; risk premiums emerge from price discounts; arithmetic vs geometric averages and the compounding drag, all formalized here), M3.01 (PV mechanics, perpetuities and the Gordon growth formula; the implied-ERP method is a Gordon/two-stage model run in reverse; real vs nominal via Fisher), M2.03 (ROIC vs a cost-of-capital hurdle, and this module builds the hurdle), and Phase 1 generally (you will read "dividends + buybacks" off cash flow statements without blinking).

Feeds forward. M3.03 consumes everything here: the ERP and CRP become inputs to the full WACC build, beta gets rebuilt bottom-up from business fundamentals, and the clean-INR risk-free fix previewed here is executed properly there. M3.04–M3.05 discount cash flows at rates this module prices; the reverse DCF of M3.05 is the implied-ERP idea applied to a single stock. M7 (macro) explains why the risk-free rate and the ERP move; Phase 9 returns to diversification as a portfolio decision (concentration vs diversification, hidden correlation) rather than a pricing argument. The mini-project's ERP card becomes a standing input to every valuation you build for the rest of the program.

The one-sentence version of this module. Investors hold a diversified portfolio, so the only risk they can charge for is co-movement with everything else; the market-wide price of that risk is the equity risk premium (a live, observable-by-inversion number, not a textbook constant), and a country like India adds a measurable surcharge on top.

4.1 The question this module prices

At a 10% discount rate, ₹100 crore arriving in year 10 is worth ₹38.6 crore today. At 13%, it is worth ₹29.5 crore. A quarter of the value, gone from three points on one dial.

Strip valuation to its skeleton: value = expected cash flows, discounted at a rate that compensates for waiting and for doubt. Phase 2 taught you to judge the cash flows. M3.01 taught you to discount. What remains is the doubt dial, and it is worth being precise about what turning it does. Get the rate badly wrong and no amount of careful forecasting saves the valuation.