Estimating Risk Premiums In Practice
Prof.&Emiliano&Pagnotta
epagnott@ic.ac.uk
Autumn&2016
Corporate(Finance
Estimating(Risk(Premiums(in(Practice
1. Survey&investors&on&their&desired&risk&premiums&and&use&the&
average&premium&from&these&surveys.
2. Assume&that&the&actual&premium&delivered&over&long&time&
periods&is&equal&to&the&expected&premium&-i.e.,&use&historical&
data
3. Estimate&the&implied&premium&in&todays&asset&prices.
What(is(your(risk(premium?
Assume& that&stocks&are&the&only&risky&assets& and&that&you&are&offered&two&
investment& options:
a&riskless&investment&(say&a&Government&Security),&on&which&you&can&make&3%
a&mutual&fund&of&all&&stocks,&on&which&the&returns&are&uncertain
How&much&of&an&expected& return&would&you&demand&to&shift&your&money&from&the&
riskless& asset&to&the&mutual&fund?
a. Less&than&3%
b. Between& 3%&-5%
c. Between& &5%&-7%
d. Between& &7%&-9%
e. Between& 9%-11%
f. More&than&&11%
The(Survey(Approach
Surveying&all&investors& in&a&market&place&is&impractical.
However,&you&can&survey&a&few&individuals& and&use&these& results.&In&practice,&this&
translates& into&surveys&of&the&following:
The&limitations& of&this&approach&are:
There&are&no&constraints&on&reasonability&(the&survey&could&produce&negative&risk&
premiums&or&risk&premiums&of&50%)
The&survey&results&are&more&reflective&of&the&past than&the&future.
They&tend&to&be&short&term;&even&the&longest&surveys&do¬&go&beyond&one&year.
The(Historical(Premium(Approach
This&is&the&default&approach&used&by&most&to&arrive&at&the&premium&to&use&in&the&
model
In&most&cases,&this&approach&does&the&following
Defines&a&time&period&for&the&estimation&(1928-Present,&last&50&years...)
Calculates&average&returns&on&a&stock&index&during&the&period
Calculates&average&returns&on&a&riskless&security&over&the&period
Calculates&the&difference& between& the&two&averages&and&uses&it&as&a&premium&looking&
forward.
The&limitations& of&this&approach&are:
it&assumes&that&the&risk&aversion&of&investors&has¬&changed&in&a&systematic&way&across&
time.&(The&risk&aversion&may&change&from&year&to&year,&but&it&reverts&back&to&historical&
averages)
it&assumes&that&the&riskiness&of&the&riskyportfolio&(stock&index)&has¬&changed&in&a&
systematic&way&across&time.
Historical&data&for&markets&outside&the&United&States&and&the&U.K.&is&more&limited
The(Historical(Risk(Premium:((Evidence(from(the(United(States
If&you&are&going&to&use&a&historical& risk&premium,&make&it
Long&term&(because& of&the&standard&error)
Consistent& with&your&risk&free&rate
A&compounded&average.&For&long-term&analysis&geometric& avg.&is&better.
No&matter&which&estimate& you&use,&recognize&that&it&is&backward&looking,&is&noisy
and&may&reflect&selection& bias.
Historical
premium for the
US
Std Error in estimate = Annualized Std deviation in Stock prices
Number of years