*Price, Risk, and Return. 3 concepts which form the very foundation of Investment Analysis & Portfolio Management. Mastering these 3 concepts will change the way you look at investments, forever.*

## What is price?

The price of a stock is typically what you pay to buy or sell the asset in the open market. You might refer to it as the market price, or the market value.

Now, we typically compare this market price to what we call the “intrinsic price” or the “intrinsic value”. And that’s the price at which the stock *should* trade at.

The intrinsic price should be based on firm fundamentals, including the amount of money the firm makes, how risky the firm is, what industry it operates in, its growth prospects, are and a whole host of other factors.

The market price may well trade at the intrinsic price, but it doesn’t necessarily have to.

You might well have a case where the market price is *greater* than the intrinsic price, in which case we’d say that the stock is *overvalued*.

And likewise, if the market price is *lower* than the intrinsic price, then we’d say that the stock is *undervalued*

Finally, if the market price is *equal* to the intrinsic price, then we say that the stock is *fairly priced*. It’s trading at its fair value.

## What is Return?

Now let’s turn to what return means.

Return refers to the amount of money that you can make from your investment, expressed in percentage terms.

So if the return on a stock is say, 10 percent, that means that you’ve earned 10 percent by investing in the stock. Put differently, if you invested a thousand dollars in a stock, that 10 percent would mean that you made a hundred dollars.

But rather than saying you made $100, we would say that you’ve made a return of 10 percent.

So ultimately then, the return is just the amount of money that you make expressed in percentage terms.

## What is Risk?

Last but not least let’s talk about what risk is.

Risk is an interesting one, because it can have many definitions many meanings. And there are a lot of ways to go about measuring or quantifying risk.

In an academic study back in 2008, Ricciardi listed about hundred and eighty different types of risks in the traditional as well as behavioural finance literature.

Now of course within these 188 a lot of them aren’t “generally accepted” measures of risk. They might be new ideas that people are trying and testing out.

And you’ll also have your classic measures of risk which are “generally accepted” across the board, at least in finance.

So we’re going to focus on the ones that are generally accepted, but it’s important for you to know that that’s not the be all and end all.

And you know there are all these other types of risks that we might consider for our individual portfolio analysis.

Now, while there are so many different types of risk, the general consensus is that it’s the likelihood or the value of you losing your money.

So each method is trying to tell you this “likelihood” or value of losing money, and it’s just doing so using different metrics or different measures.

But the ultimate “story” is exactly the same for most if not all measures of risk.

What’s really important for you is to not get bogged down in the nitty gritty details (just yet), but to understand the broader, big picture implications of price, risk and return.

## The relationships between Price, Risk, and Return

These three factors share incredibly powerful relationships. And knowing and fully understanding these relationships is vital – it’s absolutely crucial – to conducting really great investment analysis and portfolio management.

And so I’m going to spend a little bit of time now helping you really see and thoroughly understand these incredibly powerful relationships.

### The Law of One Price & Arbitrage

Consider two completely identical stocks: Arthur Plc and Conan Plc.

They both have an expected return of 10 percent.

This means that if you were to invest in Arthur Plc, you expect your money to increase by 10 percent. If you bought a thousand dollars of other Arthur Plc’s stock, conditional on this being true, you’d expect to earn $100. Because that’s 10 percent of your investment, and you expect to earn exactly the same amount by investing in Conan Plc because it has the same expected return.

Now, the risk of the two stocks is also completely identical at 15 percent.

Further assume that the price of the Arthur Plc is known to be $100.

If all of that is true, how much would you pay for Conan Plc?

It’s a good idea to pause reading right now, and try and think about how much you are willing to pay for Conan Plc.

Hopefully you did that; and what you likely thought was that, given that these two stocks are identical, and they have exactly the same payoffs (the expected returns), and exactly the same risk, they should be trading at identical prices.

In other words, you should be willing to pay *no more than* $100 for Conan Plc, because the stocks are completely identical. And so their prices must be identical as well.

This is ultimately because of the Law of One Price, which says that if you’ve got any two assets that are identical in all aspects, and they have exactly the same payoffs and exactly the same risk, then they should have exactly the same price. That’s the Law of One Price.

If it doesn’t hold… i.e., if the *prices aren’t equal* then an *arbitrage opportunity* exists.

And what that means is that you can earn guaranteed money, risk free, with zero investment.

It’s like everyone’s dream.

And to see how this would work, consider this scenario.

Imagine Arthur Plc was in fact trading at $100, but Conan Plc is trading at $110.

With this scenario we can conclude one of two things quite confidently.

We can either conclude that Conan Plc is* overvalued* and that the fair price is indeed a $100. So Conan Plc should be trading at $100.

Or we can conclude the Arthur Plc is *undervalued* and that the fair price is actually $110.Aand so Arthur Plc should be trading at $110.

Obviously, because we don’t have any other information, we can’t say which is the “right price”.

But what we can say, is that the two prices *must be equal.* And if they’re not, then an *arbitrage opportunity* exists.

Rational investors will thus either “go long” (which is a fancy word for essentially saying they would *buy* stocks in Arthur Plc). Or they would “short” (which is a fancy word for *sell*) stocks in Conan Plc at $110.

They might of course do both, which is a process called *hedging* – which is likely the optimal thing to do. That’s because we don’t know which is the correct price or the fair price.

And so the best bet in this scenario would be to hedge.

So you would buy Arthur Plc, and you would short Conan Plc.

And the likely result would be that the fair price would *probably* be somewhere in between – maybe $105.

But I don’t know. And it’s not necessarily that because like I said, the fair price could be $110 or it could be $100.

### Mispricing & Price Convergence

The point is that if you have two identical stocks with different price points, then an *arbitrage opportunity* exists.

There’s a *mispricing* in place.

And so there’s money to be made.

Now let’s think about what would happen if rational investors did indeed buy Arthur Plc and short Conan Plc.

This influx of demand and supply would cause the prices to change and so ultimately, both stock prices will converge. They’ll trade at exactly the same price.

And again, because we don’t know the true fair price, there are now two possibilities.

The price will either be $100 for both stocks, or it’ll be $110 for both stocks (or, strictly speaking, some other value).

But you won’t have a situation where one trades at $100 and the other trades at something else.

Because that would violate the Law of One Price.

An *arbitrage opportunity* would emerge, and investors (or what we call *arbitrageurs*) would exploit this arbitrage opportunity by buying the stock that’s priced lower, and short selling the stock that’s priced higher.

The resulting demand and supply would cause the prices to change. And ultimately you’d have a price convergence.

All right. Hopefully that makes sense.

### Impact of Risk on Price

We’ve seen what happens when two stocks are *identical.* But what happens when they’re not identical?

Consider two stocks that are *similar.* Conan Plc (which we know), and a new company, Doyle Inc.

Conan Plc still has the same expected return (10 percent), and Doyle Inc also has the same expected return at 10 percent.

The risk of Conan Plc is still 15 percent. But Doyle Inc has a risk of 20 percent (which is obviously greater than 15 percent).

If Conan Plc is trading at $100, how much would you pay for Doyle Inc?

Again, it’s a good idea to pause reading for now, and try and think about how much you would pay for Doyle inc.

You don’t necessarily need to come up with a specific number.

You could just think about whether you would pay *more* than $100, or whether you’d pay *less* than $100, or whether you’d pay $100 itself.

All right. Hopefully you took some time to think about how much you would pay.

Let’s go ahead and analyse this scenario together now.

Because Doyle Inc is *riskier,* it’s actually *worth less* than Conan Plc.

So you should be willing to pay *less* than $100 for Doyle Inc.

In other words, the fair price of Doyle Inc should be lesser than $100 because risky assets are worth less than safer assets.

And this is intuitive.

If Conan Plc is less risky, then that’s a safer investment for you. And therefore, you’re willing to pay more for a safer investment.

Since Doyle Inc is more risky, you’re willing to pay – or you *should* be willing to pay – less for the same company.

Because the returns for the two stocks are identical. But Doyle Inc is more risky. So the chances of you getting this 10 percent are smaller or are lower than if you were to invest in Conan Plc.

Given the higher risk therefore, Doyle Inc should be worth less.

Now let’s consider another scenario.

We’ve still got Conan Plc, which has a return of 10 percent and a risk of 15 percent. The price is $100.

But now we’ve got Lock Inc, which has the same expect return as Conan Plc, but has a risk of 8 percent – significantly lower than the risk of Conan Plc.

Pause reading now.

And just quickly think about how much you’d be willing to pay for Lock Inc.

Hopefully this should be quite very clear.

Because Lock Inc is *less risky* compared to Conan Plc, we should be willing to *pay* *more* for Lock Inc.

So the price should be *greater than* $100. And that’s because safer assets are worth more than riskier assets.

And this is consistent with what we saw before.

So when we looked at Conan Plc and Doyle Inc, Conan Plc was the safer of the two. And it should have been worth more than Doyle Inc.

With Conan Plc and Lock Inc – Lock Inc is the safer company. and therefore Lock Inc should be worth more than Conan Plc.

And this relationship is an incredibly important and powerful one.

It is that the value of an asset increases as the risk decreases; and conversely, the value of an asset decreases as the risk increases.

Now if we think about risk and return, or risk and expected return on the other hand, they maintain a proportional relationship. Such that as risk increases, the expected return increases. And as risk decreases, the expected return decreases.

Crucially, and I really can’t stress this enough… we’re talking about expected returns here, *not returns*.

## Wrapping up

Higher risk does not necessarily mean higher returns.

If that were true, then the richest people in the world would be gamblers.

High risk can indeed have a significantly adverse consequences.

So we’re talking about expected returns here, which is *very different* from returns.

If a stock is highly risky, then in order for us to invest in it, we will demand a very high return.

And if a stock is less risky, then in order to invest in it, we’re happy to accept a lower rate of return (because our money is safer).

All right. Hopefully that makes sense. Let’s just have a quick recap of this powerful relationship again.

As risk increases, the expected return increases, but the price (or the value) decreases.

And as risk decreases, the expected return decreases, but the price (or the value) increases.

Do take the time to know and fully understand this relationship. Because it will hold you in good stead, no matter what investment you’re making, no matter where you are in the world.

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