Behavioral finance FAQ / Glossary (Risk premium)

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Dates of related message(s) in the
Behavioral-Finance group (*):

Year/month, d: developed / discussed,
i: incidental

Risk premium

00/5d, 6i,12i - 01/9i,11i - 02/9i
- 03/8i - 04/2d - 05/5i - 06/11i
- 07/1d,2d
+ see utility, risk,
risk aversion, equity premium
puzzle, risk premia puzzle

High return for risky stuff.

The price of fear?

based on returns

based on prices

To put it simply, in investment matters,
the risk
premium is a monetary 
reward for monetary

More formally and in the most usual

The risk premium is a return
between a risky
and a safe one offering
   the same
expected incomes

It is thus a monetary bonus,
added by
the market to the
expected return (*)

(*) A return which is already risk-
     adjusted, by
using probabilities:
     see "expectation".

The risk premium does not
just compensate a risk
, it is
bonus to overcome the risk

This is done via a lower asset
(see next column).

The price does the trick:

bargain price
high return

As returns are linked to prices,  
the risk premium comes from the
difference between.

The asset's market price


The expected

of its projected revenues
(cash flows) when discounting
them with a riskless rate of return

A lower buying price gives a
higher return

 This is pure mathematics, as:

If an asset
- offers an income I
- and is sold at a price P,
=> its return R = I / P
is higher when P is lower.

Why this premium?

Give me a bonus,
a carrot to overcome my aversion!

As seen in the "risk" and "risk aversion" articles, investors usually want
a better return for assets they consider risky.

Therefore, risky investments are supposed to earn
more than
safer ones, even after the expected
incomes are adjusted by taking into account the
probabilities (aka "risks").

The difference - the risk premium can be considered to measure

the average risk aversion for all investors and for a
whole asset market in a given period.

Unlike gamblers, who pay the casino for their risk taking, investors
get paid - at least in the long term and in average - for their risk

What is affected, when and how?

Any idea how I can get the bonus
if put my nest egg on a risky branch?

Technically, that bonus takes the form of an extra return, a - normally
positive - difference in returns

Between investments seen
risky vs. those seen as

The risk differs according to the
type of investments (asset class).

For stocks (to take an example),
expected revenues are uncertain, thus
they are quoted at a low price

Thus, in the long term, after some ups
and downs, stocks usually bring a
higher average return than high-
grade bonds
(sovereign bonds from
a solvent country), with expected
revenues seen as certain.

This average stocks vs. bonds
extra return
the equity premium.

Also between investment

are seen as
(bear mket)

vs. periods
are deemed
less risky
(bull mket)

Therefore the risk premium
is variable

It might even be negative
when we see a bubble, as
market rationality has then
gone to vacation.

In practice, this higher return is obtained through a lower buying price,
as seen above.

The family: uncertainty premium, risk premium,
    equity premium, beta...

The risk premium has brothers and sisters.

The risk premium is computed usually as the average extra return of
a whole class of traded assets.

Actually, it should be called the "uncertainty premium" because
risk, a probabilistic notion, however useful, is not fully reliable and
measurable for many assets.

Asset markets, and markets in general, show a degree of uncertainty
(see that word).

It can override what "stochasticians" (see stochastic) compute as risk.

For example, past volatility is just a
proxy for future risk. Thus take it with precautions
when doing financial projections.

Stochastics, based on historical probabilities and classical statistical
distribution laws (randomness), save the effort to make scenarios but
they are limited substitutes.

Of course, high volatility can be associated to high uncertainty,
notably when crashes strike:

Crash --> uncertainty

Uncertainty --> volatility

Volatility --> more uncertainty

More uncertainty --> rise in the uncertainty premium

Rise in the uncertainty premium -->crash persistence

And so on.

For a
stock market, as seen above, the risk premium is usually called
the equity premium.

It is measured normally on the basis of a wide enough stock sample,
usually a stock index covering several hundred stocks.

But this aggregated premium related to the whole market is modulated
for individual assets by the "beta coefficient"
(see that phrase).

A tip and a puzzle.

The risk premium, at least for long term investment, is an
incentive for investors to prefer a portfolio of risky assets to one of
safe assets.

It is often advised, except in highly uncertain periods (for example
     when a bubble lasted for too long), to have few bonds (mainly as a 

liquidity tool) and plenty of stocks, so as to take advantage of the
equity premium

OK, but with two conditions:

To diversify our holdings according to broad countries /
   industries / corporations,

And, better say it again, to take the exit

discreetly when a bubble becomes obvious because the risk
premium schrank

Leave the party when it could get nasty!

Another thing is that the risk premium, or more specifically the equity
premium, although a standard finance notion, raises various puzzles (see
risk premia puzzles).

Risk premia puzzle


00/5d, 6i,12i - 01/9i,11i - 02/9i
- 03/8i - 04/2d - 05/5i - 06/11i
07/1d,2d,5i + see utility, risk,
risk aversion, risk premium,
equity premium puzzle

The risk premium raises quasi metaphysical questions:

Can it be measured?
What is its "normal" level?
And more iconoclastic, should it exist?

As said in the risk premium article,

That premium, or more specifically the equity premium,

although a standard finance notion, raises various puzzles

1) Puzzles linked to measuring the premium

Rubber yardsticks for rubber data.

The first issue is that the equity risk premium can be
measured only ex-post, by comparing the performances,

for example between:

Dividends + price rises (minus price falls) for stocks,

Essentially interest coupons for (safe) bonds (*).

(*) Sovereign bonds are the usual reference for riskless assets,

although there might be some illusions nowadays about their safety.

Maybe another reference has to be found, something linked to
growth rate and monetary inflation.

On the other hand, the current premium cannot be directly
measured. It can only be estimated as it is based on future return

Btw, what about the "equity premium", in average for all stocks

stocks as an asset class, therefore without taking into account
individual "beta coefficients" (see that phrase)?

What parameters can measure / estimate current
equity risk premia?
(defined again as added returns)

Expected price evolutions for the related assets?

But that would be pure circularity (as stocks have lower price,
they have more potential to rise), with crystal ball added!

Well, it would fit the return part in the risk premium theory.


=> The risk premium fluctuation is only apparent

      when low or high prices show

* low or high price expectations 

* rather than high or low risk aversion.
interference is frequent.

Discounted Expected dividends or cash flows  (see 

"expected value") are good candidates. But

  * they are also estimates, not direct measures,

  * they are far from easy to evaluate for the whole asset class.

A simplistic caricature, numerology at its best - but rather

widely used for stocks - is to take the difference between:

* The current earnings yield (the reverse of the P/E),

Stock holders do not receive directly in full those earnings,
the firm keeps a part for whatever purpose.

* And the sovereign bonds interest rate!

2) Puzzles linked to the level of the premium

How high it is? How high should it be?

When does it makes the market dizzy?

Another puzzle is that the premium is not a constant but a
that expresses that the collective "risk aversion" varies
in time
and space.

That premium can even be negative for some "glamour" assets, or during some
"exuberant" periods.

Not only you cannot really trust the "historical" risk premium data, but
also all this raises several other questions:

Is the premium related to the real risk?

Does the risk premium theory reflects the real world?

Or to be more precise, is the risk premium related to the
general market uncertainty?

You know, the possible danger you cannot measure and that
has  no reliable / objective probabilities.

As this premium is (highly) unstable, are its variation's
its extreme value predictable?

When market prices move largely, how to know in what
proportion to attribute the move to the premium variation?

Or to other economic and market parameters?

Or to changes in the risk and return expectations

What about economists who consider the premium as
stable,  and the rest of the Universe to move around?

How high should the 'normal' risk premium be in  
average for a typically risky asset (equities for example)?

Should it make the return rate be at least the double or
triple of the riskless rate?

That would seem justified if we apply blindly the
theory" or "loss aversion theory", which
address slightly different phenomena: see the related
glossary articles.

Or just take 6 percentage points in average (for stocks)
as various economists suggest?

If the long term riskless rate is 5%, the risky rate would
be 11%. Or more precisely 1.05 x 1,06 -1 = 11,03 %.

But why should the risk premium match a precise number,
independently of the asset's nature and of the actual state
of affairs?

Why suppose that people aversion for risk and feeling of
uncertainty are intangible as predefined for ever?

3) The specific "equity premium puzzle"

What insurance premium for stock risk?


The "equity premium puzzle" (or "equity risk premium
puzzle" (see that phrase) is about the risk premium included in
stock prices and returns compared to riskless assets
sovereign bonds as a reference).

Why should it exist? As for a diversified portfolio and for the long term,
the risk is normally neutralized.

Here several puzzles appear :

The existence of an equity premium does not seem rational when

looking at the long term.

It contradicts a bit the fact that equities give better long term
return without real long term risk (*)

  If that premium is large, which seems to be the usual case, how to

       explain that apparent excessive risk aversion by

  What if the assumption that a diversified portfolio is more risky
investing in sovereign bonds was a bit far fetched, as long as
      investors add some
timing precautions when managing that
      portfolio so as not be caught in some asset bubble?

What if the EP had nothing to do with risk aversion (**)

and was hiding other, more complex phenomena (***)?

Last but not least, what if the equity risk premium was a
    statistical illusion?

(*) Well, maybe the investor want to see the return before dying ;-)

(**) A person who invests for the long term (i.e for retirement)
prefer to do it on equities than in bonds. Its reluctance

to do it, by preferring bonds anyway, is seen as a behavioral

bias called the myopic loss aversion.

(***) See underreaction, overreaction, image coefficient...

An added problem for equity premia is that there are many ways to

calculate stock returns (taking into accounts dividends, cash
earnings, earnings, stock price gains, etc.).

Depending on the calculation method,

the average historical EP (equity premium)

is said to be somewhere between 3-4 % and 7-8 %.

3b) In reality there might be some
(weak? strong?) rationale in the EP.

The future takes time, you know

Those "puzzles" may overlook the fact that some rational motivations
would explain and justify the equity risk premium.

Those motivations would be linked to the following factors:

The short term volatility, but also the ever

   present possibility of sudden crashes:

To lose money fast is not better - it is even worse - than
losing it slowly!

In "secular bear markets", a very long time might be needed to
   offset the loss.

It might take a full human generation time span before getting even and
receiving a
return comparable to some safer assets.

Other interferences

 The devil is in the details.

Without digging too much deeper, we might cite other
           interferences that complicate the analysis:

The modern portfolio theory complicates somewhat the approach:

It assimilates reductively, and abusively, at least when it is used
in a naive and lazy way, future risk and historical volatility (*).

A stock yield is harder to define, and to predict, than a bond yield.

The stock yield depends on the payout ratio (dividends vs.
earnings) and the market performance (which includes capital

The tax treatment is not the same for bonds and stocks.

Inflation and money illusion (see that phrase) interfere.

When the market price rises and falls, what is not always obvious is

whether it means a change in:

 * investors attitude (thus in the risk premium),

 * or asset fundamentals.

(*) Or, in some equations, "implied volatility" a parameter deducted from
     the option market quotes,
but nothing proves that it mirrors the real risk.


(Related topics)

Risk (vs. uncertainty)

See specific page

Risk attitude, aversion, perception....

See specific page

(*) To find those messages: reach that BF group and, once there,
      1) click "messages", 2) enter your query in "search archives".

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This page last update: 24/09/15  

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