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This tutorial written and reproduced with permission from Peter Ponzo

Recently I was asked whether buying a stock for a few percent less would make much difference in your annual return and I said I didn’t think so because …

#### Buy for less? What does that mean?

I mean instead of paying, say, \$10 and 11:30 AM you manage to buy it for \$9.50 at 3:30 PM. Would that make much of a difference at year’s end?

#### From \$10 to \$9.50? That’s a 5% decrease so I’d say the difference is peanuts.

Yeah, that’s what I said. In fact, if the stock went from \$P to \$Q in one year, your Annual Return is Q/P – 1. For example: from P = \$10 to Q = \$11 the return is 11/10 – 1 = 0.10 or 10%. Now, if you bought it at \$9.50 your return would be: 11/9.5 – 1 = 0.158 or 15.8%.

#### That’s not peanuts, eh?

No, it isn’t. In fact …

Roughly. In fact, if the stock went from \$P to \$Q then the return is Q/P-1. However, if you managed to buy the stock at less than \$P, say at P(1 – R), where R = 0.05 means 5% less, then your return becomes Q/{P(1-R)}-1 which is roughly Q/P-1 + R.

For different price reductions (R running from 2% to 8%) the increased annual return is shown in Figure 1.

Figure 1

#### Huh?

The plot is the increased return: Q/{P(1-R)}-1 versus the stock return: Q/P -1. For example, if the stock return from \$P to \$Q is 15% and you managed to buy the stock for 8% less than \$P, you’d get a 25% return.

The red dot.

#### Red? Aah, but there’s a grey dot.

That’s the example we started with: P=\$10, Q=\$11 hence a 10% return … compared with the return when we buy at 5% less than P.

Good luck.