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 Allocation
5 conceptsExpected return of a blended allocation
A portfolio’s expected return is simply the average of its parts, weighted by how much money sits in each. That makes it the one portfolio number that is easy — and it is why the allocation decision dominates everything else an adviser does. Moving ten points from bonds to equities changes the expected return by a tenth of the gap between them, every year, for as long as the client holds it. Fees come straight off the top of that blend. Run the calculation backwards and it answers the question clients actually ask: how much equity do I need to hit the return my plan assumes?
Rebalancing trade size
Markets move the allocation for you. After a strong year for equities a 60/40 portfolio might be 66/34, carrying more risk than the client signed up for; after a crash it might be 50/50, carrying less. Rebalancing is the discipline of trading back to the agreed mix: selling what has done well and buying what has done badly. That feels wrong, which is exactly why it has to be a rule rather than a judgment call. The trade size is the gap between what the client holds and what the target says they should hold on today’s value, and new contributions can close that gap without selling anything.
Glide path
A 25-year-old’s biggest asset is forty years of future salary, and a bad decade in the market barely touches it. A 64-year-old’s biggest asset is the portfolio itself, and a bad year just before retirement can be permanent, because withdrawals start while prices are down. A glide path turns that into a schedule: lots of equity early, less each year, a floor at retirement. Target-date funds are exactly this. The arithmetic is a straight line, and the questions worth asking are how steep it is, what it means in dollars this year, and what moving the retirement date does to it.
Two-asset risk and return tradeoff
Every allocation is a point on a curve: more equity buys more expected return and costs more volatility. But the curve is bent, not straight, because stocks and bonds do not move in lockstep. That bend is why a little bond in an all-equity portfolio removes a lot of risk and very little return. Clients do not think in volatility, so the adviser translates: a one-in-twenty bad year, in dollars, is a number a client can decide whether they could live with. Run it backwards and the client’s tolerance for a bad year sets the equity weight.
Hedged versus unhedged international
An American who buys European shares makes two bets at once: one on the shares, and one on the euro. If the shares rise 8% but the euro falls 6% against the dollar, most of the gain disappears on the way home. Hedging removes the currency bet by selling euros forward, and the price of doing so is set by interest rates, not by anyone’s view of the euro: when dollar rates are higher than euro rates the hedge actually pays. For equities the currency adds a moderate amount of risk; for bonds it can swamp the asset entirely, which is why most advisers hedge foreign bonds and argue about foreign equities.
Retirement Planning
5 conceptsFuture value with regular contributions
Retirement saving is two engines running at once: the balance you already have, compounding, and a stream of new contributions, each of which compounds for a shorter time than the one before. Early on the contributions do almost all the work; after a couple of decades the growth on the balance overtakes them, and by the end most of the money in the account was never contributed at all. That is why the cost of starting late is so much bigger than the missing contributions — the dollars skipped were the ones that would have compounded longest.
Safe withdrawal rate
A retirement portfolio is a race between what it earns and what the client takes out. If the withdrawal is no bigger than the real return, the money never runs out; every dollar above that is eaten out of capital, and the capital then earns less next year, so the decline accelerates. The famous 4% rule is a rough answer to "how much can I take, rising with inflation, and still survive a bad sequence of markets over thirty years?" Constant-return arithmetic understates the danger, because it never has a crash in year two — but it is the right place to start, and the right way to see how sensitive the plan is to the return.
Required savings rate
Every retirement plan reduces to one number the client controls: the share of salary they save. Work backwards from the income they want in retirement, the years it must last and the return they can expect, and the plan tells you the pot they need on the day they stop working. Work forwards from their salary, years of work and the same return, and it tells you what each point of savings builds. The required rate is where the two meet. Its most useful property is how violently it responds to the retirement date: working a few years longer both adds contributions and removes withdrawals, so it moves the rate far more than any plausible change in returns.
Claiming-age tradeoff
Claiming a public pension early buys more years of checks at a permanently smaller size; waiting buys a bigger check for fewer years. The early claimer races ahead, and the late claimer catches up a little every month, so there is an age at which their cumulative totals cross. Live past it and waiting won. Framed that way, claiming is a bet on your own longevity — and, because the delayed benefit is inflation-linked and lasts for life, it is also the cheapest longevity insurance most retirees can buy. For a married higher earner it doubles as a larger survivor benefit.
Real versus nominal returns
A retirement plan is a promise about what money will buy, not how many dollars there will be. Inflation quietly converts one into the other: at 3% a year, a dollar buys about half as much in twenty-four years. The return that matters is therefore the real return — what is left after prices rise — and for anything held in a taxable account, what is left after the tax on the nominal return as well. That second step is the one clients miss: tax is charged on the part of the return that merely kept up with inflation, so a bond yielding comfortably above inflation can still lose purchasing power once the tax bill arrives.
Tax & Fees
4 conceptsFee drag compounded
A 1% fee sounds like 1% of the money. It is actually 1% of the money every year, and each year’s fee also removes the growth that money would have earned for every year after. Over thirty years that compounds into a quarter of the client’s ending wealth — and a far larger share of the investment gain, because the fee is charged on the capital as well as the return. That is why the fee is the most reliable predictor of net returns an adviser has: markets are uncertain, costs are not. The same arithmetic tells you how much an active manager must beat the market by, every single year, just to stand still against an index fund.
Tax-loss harvesting
When an investment is below what the client paid for it, selling turns a paper loss into a tax deduction without changing their market exposure — they buy something similar with the proceeds and stay invested. The deduction is not free money: the replacement now has a lower cost basis, so the loss comes back as a bigger gain when it is finally sold. What harvesting really buys is time. Tax is paid later instead of now, the saved tax compounds in the meantime, and if the client’s rate is lower later — or the position is never sold — the deferral becomes a permanent saving. The traps are the wash-sale rule and forgetting that losses offset gains before ordinary income.
Taxable-equivalent yield
A municipal bond yielding 3.5% can beat a corporate bond yielding 5%, because the investor keeps all of the first and only part of the second. The taxable-equivalent yield puts them on the same footing: the taxable yield the client would need to end up with the muni’s income after tax. It rises with the tax rate, which is why munis are a high-bracket product — and why holding them inside an IRA, where the tax break is wasted, is a classic mistake. The break-even tax rate turns the comparison into a single question: is this client’s marginal rate above or below it?
Roth versus traditional
A traditional account takes the tax break now and pays tax on the way out; a Roth pays the tax now and lets everything out tax-free. Multiplication does not care about order, so if the tax rate is the same at both ends the two produce exactly the same after-tax money — the growth is sheltered either way. The whole decision is therefore a bet on one number: is the client’s tax rate higher today or in retirement? The one wrinkle is contribution limits. A dollar in a Roth is worth more than a dollar in a traditional account, so when the client can only put in a fixed amount, the Roth shelters more money.
Risk Profiling
3 conceptsRisk capacity versus risk tolerance
Two different questions hide inside "how much risk should this client take?" Tolerance is psychological: how big a loss can they watch without panicking and selling at the bottom? Capacity is financial: how big a loss can the plan absorb before essential spending is no longer covered? A wealthy, nervous client has plenty of capacity and little tolerance; a bold client with a thin cushion has the reverse. The adviser’s job is to measure both and let the tighter one set the limit — because exceeding tolerance leads to bad behavior, and exceeding capacity leads to a plan that fails.
Drawdown recovery
Losses and gains are not symmetric. Fall 20% and you need 25% to get back; fall 50% and you need 100%. The deeper the hole, the faster the required gain grows, because it is earned on a smaller base. That arithmetic is the most useful thing to show a client when setting risk levels: it turns an abstract drawdown into years of waiting. Withdrawals make it much worse, because money taken out during the recovery never participates in it — which is why the same drawdown that is an inconvenience for a saver can be permanent for a retiree.
Time horizon and equity weight
Equities are risky over a year and much less risky over twenty — not because the bad years stop, but because they get averaged with good ones. The expected return piles up with time while the noise in the average return shrinks with the square root of time, so the chance that a long holding period ends in a loss falls steadily. That is the honest case for more equity when the money is not needed for decades, and the honest case against equity for money needed in two years. It is a statement about averages, though: a long horizon lowers the chance of losing, but not the size of the worst outcomes, and the dollar amount at risk still grows.