Risk and return: no reward without risk

Two envelopes sit on the table. The first is guaranteed: open it next year and find £105, no matter what. The second is a coin flip — heads £140, tails £80. Which do you take?

The second envelope averages £110 — more than the guaranteed £105. Yet your hand hesitates over it, because you might open it and find only £80. That hesitation is the whole of finance in miniature. The extra £5 of average that the risky envelope dangles isn’t a gift. It’s a payment — for making you sweat.

You’ve now met two things to own: a share (an owner’s wild ride) and a bond (a lender’s steadier one). This item explains the force that sets them apart, and prices everything in the market: risk.

Return is what you get. Risk is how sure you are.

Return is plain: it’s what your money earns, as a percentage. Put in £100, get back £108, that’s an 8% return.

Risk is the part people get wrong. Risk is not simply “the chance of losing money.” Risk is the spread of what could happen — how wide the range of outcomes is. The risky envelope might pay £140 or £80; that whole fan of possibilities, good and bad, is its risk. Something that could land anywhere from −20% to +40% is risky even though it might end wonderfully, because you cannot know in advance where in that fan you’ll land. Width, not just downside.

A guaranteed £105 has zero spread — one outcome, known. The coin flip has a wide spread. Same money at stake; different risk.

Why reward and risk are chained together

Here is the law that holds the market up. Suppose a safe thing and a risky thing offered the same average return. Everyone would take the safe one — why accept the sweat for no extra reward? Nobody would hold the risky thing. So its price would fall until, cheaper, it offered a higher return — enough extra to tempt someone into bearing the uncertainty.

That extra is called the risk premium: the additional average return a risky asset must pay to get anyone to hold it. The market sets it, constantly, through exactly that push and pull. It means the chain runs one way and can’t be cheated: you cannot get a higher expected return without accepting a wider spread. Anyone promising high returns with no risk is selling the one envelope that doesn’t exist.

This is why a share (item 1) is chained to more risk than a bond (item 2). The owner gets paid last and rides every up and down; the lender gets a fixed coupon and gets paid first. So the share must offer a higher expected return, or no one would prefer the wilder ride. Over long stretches of history, that’s exactly what stocks have done — paid more than bonds on average. Not magic. Rent for the spread.

A worked example: the gap, and the catch

Picture two ways to hold £10,000 for a year.

• A government bond: returns about +4%, almost dead certain. Your fan of outcomes is a narrow sliver around £10,400.
• A basket of stocks: returns about +8% on average — but any single year ranges roughly from −30% to +30%. A wide fan. One year you’re at £13,000; another, £7,000.

The 4-point gap between them — bond’s +4% and stocks’ +8% — is the risk premium. It’s what the stock basket pays you for the sleepless years.

Now the catch, and it’s the one that ruins people. You only collect that higher average if you can stay in through the bad years. Say the stock basket falls 30% in year one — your £10,000 is now £7,000. The +8% average is a long-run figure; it assumes you hold on while the fan plays out. Sell in the −30% year and you don’t get the average. You’ve locked in the loss and kept none of the premium. The spread didn’t just threaten you on paper; it shook you out before the reward arrived.

So the skill in markets isn’t avoiding risk — avoiding risk is the guaranteed envelope, the lowest return there is. The skill is taking risk you’re paid enough for, and that you can survive long enough to be paid. You’ll feel that exact tension in a moment: turn the risk up and watch the average climb — and the floor of bad outcomes drop with it.

The whole, not the bet

Pull back and look at the market as one thing. Every price in it is, underneath, a verdict on risk — a crowd of strangers haggling over how much extra reward a stretch of uncertainty is worth. The bond yield, the stock’s price, the premium between them: all of it is people, together, putting a number on the unknown.

You are inside that crowd whenever you save, borrow, or own. There’s a humility in seeing it. The future genuinely cannot be known, and no price, however confident, removes that — it only puts odds on it. The market doesn’t abolish uncertainty; it prices it, and asks who will carry it. Knowing that risk and reward are chained, and why, is what lets you read the rest of this course — and the rest of the market — without mistaking a wide fan of outcomes for a sure thing.