The value of shares goes up and down a lot, and all this volatility creates uncertainty for investors.  It’s not very clear, for most investors in shares, exactly what the value of their share portfolio will be at any point in the future.

We’ve been asked why shares are so volatile.  Hopefully this explanation will help.

Shares represent ownership in business.  Shareholders have a claim on the profits the business makes – these profits are paid out as dividends, or reinvested into the company in order to grow future profits.

The most basic model of valuing shares takes both of these inputs – dividends and growth (by growth, we mean growth in profits) – and combines them in an equation to form a price.

The model states that Price (P) equals the next dividend (D₁) divided by my required return (r) minus my expected growth (g).

Put together, the model looks like this:

Let’s try out the model.  We’ll say next year’s dividend is going to be $0.25 per share.  Let’s say I require a 10% return on my investment to make it worth my while, and let’s also say I expected dividends to grow at 4% per year into the future.

The model would say the price =

An investor with the assumptions above would be willing to pay $4.17 for shares.

Now, let’s alter the growth assumptions.  We’ll run one scenario where growth is 3% and another where it’s 5%.

5% growth:

3% growth:

A 1% change in growth doesn’t seem like a big deal – the company is profitable in either case – yet a 1% increase in the growth projection translated into a $0.83/$4.17 = 20% increase in price.  A 1% fall in the growth projection caused a 14% fall in price.

The point of this is to illustrate that changes in projections about future growth (even small ones) can cause big changes in prices.  In the real world, there’s a lot of disagreement about the growth potential of businesses.  This disagreement is good, as it creates willing buyers and sellers.  When buyers and sellers come to some agreement that growth prospects have improved or worsened, prices will move pretty quickly to adjust.

Should you only invest in businesses with high projected growth?

One conclusion you may be tempted to make is to only invest in businesses with high growth forecasts.

That would be the wrong conclusion.

One thing this model points out to us is that an investor should really be indifferent between an investment with 3% growth, an investment with 4% growth and an investment with 5% growth.

Why?

In each case, the price adjusts, so an investor could expect roughly the same return with any of the three growth projections.  What this means is that great companies are not always great investments, and bad companies are not always bad investments.  The important thing to consider is what you are paying to invest in either.  At the right price, you are indifferent.  In fact, evidence suggests that investments with low prices provide higher returns over the long run, even though they often have low growth projections.  This is probably because these companies have poor prospects and investors require higher returns (a higher r from the equation above) to own them.  At any rate, the model helps us understand why this would be the case.

Hopefully this has helped you understand why markets concern themselves so much with growth, and why prices can move so much and so quickly, as well as.  It should also have explained why price movements are so important.  They reset the investment equation so that firms with very different growth potential are actually comparable investments.

How would prices change if growth projections stayed constant?

While the above is useful, it may leave you with the impression that growth rates have to increase for you to get a positive return on your investment.

That isn’t the case.  Prices will still increase in a world where there is no change in growth projections.

Why?

Let’s say that growth doesn’t change.  It stays at a forecasted 4%.  What would happen to prices in that world?

Even in that case we can expect prices to appreciate because of two things:

• In this world, you received the dividend
• In this world, you achieved the forecasted growth

If growth was 4%, next year’s dividend would not be $0.25.  It would be $0.25 plus 4% growth.  It would be $0.26.

Doing the same equation as above, a business with a $0.26 dividend, 4% projected growth and 10% required rate of return would translate into a price of $4.33.  That’s around a 4% increase from $4.17.

You then add your dividend yield to this gain, which is the dividend divided by the price.

Add them together: 4% (capital gain) + 6% (dividend yield) = 10% (return).

Thus, in the default world the price will go up every year, and you’ll get that 10% return every year.  Of course, we also know that rarely occurs.  Economic cycles, business decisions, interest rates and a host of other things each year influence the prospects of businesses to grow profits.  And, if both buyers and sellers agree that growth projections have changed, prices will change quickly to reflect this fact.

By looking at investments this way you can see why shares have an expected return, where that return comes from and that it does not require improvements in forecasted growth to achieve the expected return.