Every concept, endless questions
Each concept is a small financial model. Read how it works, then draw a real interview question from it: forwards, backwards or what-if, with fresh numbers and a worked solution every time.
Forward runs a concept the usual way. Inverse runs it backwards, which is what separates understanding from memorizing.
Portfolio Risk
5 conceptsTwo-asset portfolio volatility
Risk does not add. Two positions with 30% volatility each do not make a 30% portfolio unless they move together perfectly; if they move independently the combination is far calmer, and if they move against each other it can be calmer still. The correlation is the whole story: it decides how much of each asset’s risk survives the combination. Every hedge, every pair trade and every diversified book is an application of this one formula, and the number that matters most in a crisis — when correlations go to one — is the one that is hardest to estimate.
Beta hedge ratio
A long book has a beta, and the beta is a market position the manager may not want. The cheapest way to remove it is to short index futures: each contract carries a fixed dollar exposure to the market, so the number of contracts is just the beta-dollars you want to shed divided by the beta-dollars per contract. Hedge to zero and the book’s P&L becomes pure stock selection; hedge to a target beta and you keep a chosen amount of market. The hedge is only as good as the beta estimate — and betas move, so the hedge is re-struck, not set.
Sizing under a drawdown limit
A hedge fund’s real risk limit is the drawdown at which its capital gets cut — by the platform, by the prime broker or by redeeming investors. Everything else is sized backwards from that. Start with the cushion between where the fund is and where it dies, decide how bad a bad day can be in units of volatility, and the maximum gross exposure falls out. The arithmetic has a cruel corner: after a loss the cushion is smaller, so the book must shrink just when the manager most wants to press — and the gain needed to recover grows faster than the loss that caused it.
Sharpe ratio and leverage
Sharpe measures return per unit of risk, and leverage is the dial that turns one into the other. A strategy that earns a little with very little risk can be levered into one that earns a lot with a lot of risk, and — if borrowing were free — the Sharpe would not move: both the excess return and the volatility scale by the same factor. Borrowing is not free, so each turn of leverage costs the financing spread and the Sharpe erodes a little. That is why allocators compare strategies on Sharpe and then choose how much to lever, and why a high Sharpe at low volatility is worth more than the same return at high volatility.
Contribution to risk versus contribution to capital
Half the capital is not half the risk. A volatile position in a 50/50 book can account for eighty percent of the portfolio’s volatility while the quiet one accounts for twenty. The contribution to risk is what each position adds to the portfolio’s volatility, counting how it moves with the rest of the book, and the contributions add up to the total exactly. Risk parity is the idea of sizing so that they are equal — which for two assets simply means giving the quieter one proportionally more capital. Whether or not a fund runs risk parity, the gap between the capital split and the risk split is the first thing a risk manager looks at.