Volatility

The exam’s favorite tell is a question that hands you total risk and asks which security a diversified investor should fear less. The answer hinges on one rule: in a well-diversified portfolio, idiosyncratic risk washes out, so only systematic risk (beta) is priced — a high-volatility stock with low beta (think gold miners) can still command a low CAPM required return, because its swings are largely market-unrelated. Watch the trap of pairing standard deviation with the Sharpe ratio (correct — total risk) but beta with the CAPM/SML (correct there); mixing them is the classic error. Since variance grows linearly with time, scaling uses the square root of time — doubling the horizon multiplies volatility by √2, not 2.

Don’t confuse volatility with beta (market sensitivity only) or liquidity (ease of converting to cash without moving the price). A subtle wrinkle: rarely-traded, infrequently-repriced securities can look artificially calm because stale prices smooth out true dispersion — though actively traded micro-caps usually show higher measured volatility. Memory hook: “vol = the whole bag of risk; beta = only the market’s slice.”