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Internal consistency of risk free rate and MRP in the CAPM

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average long run <strong>in</strong>flation forecast <strong>of</strong> 2.5%, based on <strong>the</strong> middle <strong>of</strong> <strong>the</strong> RBA’s target<br />

b<strong>and</strong> for <strong>in</strong>flation, this is equivalent to nom<strong>in</strong>al economic growth <strong>of</strong> 6.59%. This is also<br />

consistent with <strong>the</strong> 6.9% average expected <strong>rate</strong> <strong>of</strong> growth <strong>in</strong> dividend per share <strong>in</strong> <strong>the</strong><br />

US from 1946 to 2008. 63 By way <strong>of</strong> comparison, equivalent real growth <strong>in</strong> <strong>the</strong> US s<strong>in</strong>ce<br />

1929, 64 start<strong>in</strong>g immediately prior to <strong>the</strong> great depression, was 3.3%. If <strong>the</strong> data series<br />

beg<strong>in</strong>s <strong>in</strong>stead at 1933 <strong>the</strong> real average growth <strong>rate</strong> is 4.0%.<br />

190. The use <strong>of</strong> long run historical economic growth should be dist<strong>in</strong>guished from us<strong>in</strong>g <strong>the</strong><br />

long run historical <strong>MRP</strong> to predict <strong>the</strong> currently prevail<strong>in</strong>g <strong>MRP</strong>. In <strong>the</strong> latter approach<br />

one is us<strong>in</strong>g long run historical <strong>MRP</strong> <strong>and</strong> assum<strong>in</strong>g it is <strong>the</strong> best estimate <strong>of</strong> <strong>the</strong><br />

prevail<strong>in</strong>g <strong>MRP</strong>. This is not ak<strong>in</strong> to how I am us<strong>in</strong>g long run historical economic<br />

growth. In this approach I am us<strong>in</strong>g a long run historical economic growth to <strong>in</strong>form my<br />

view about <strong>the</strong> best estimate <strong>of</strong> a long run future economic growth beyond immediate<br />

term forecasts - which I <strong>the</strong>n use, along with current data on equity prices, short-term<br />

dividend forecasts <strong>and</strong> CGS yields as <strong>the</strong> <strong>in</strong>put <strong>in</strong>to our estimate <strong>of</strong> <strong>the</strong> prevail<strong>in</strong>g<br />

<strong>MRP</strong>. Importantly, I am us<strong>in</strong>g long run historical estimates as a proxy for long run<br />

future estimates – I am not us<strong>in</strong>g <strong>the</strong>m to proxy short run (prevail<strong>in</strong>g) conditions.<br />

63 The appropriate data for Australia is not easily accessible – not<strong>in</strong>g that it is desirable to track dividend per share growth not<br />

dividend growth per se. This means we require an estimate <strong>of</strong> <strong>the</strong> dividends an <strong>in</strong>vestor would receive if <strong>the</strong>y never<br />

re<strong>in</strong>vested dividends nor participated <strong>in</strong> share buy backs. Also, it is desirable to be able to calculate dividend per share<br />

growth on a portfolio that is constantly be<strong>in</strong>g reweighted to match <strong>the</strong> market portfolio over time. Data is available to<br />

perform <strong>the</strong>se calculations from <strong>the</strong> US. The average mean cont<strong>in</strong>uously compound<strong>in</strong>g growth <strong>rate</strong> for dividends,<br />

measured on this basis, on <strong>the</strong> New York Stock Exchange was 6.10% over this period. The st<strong>and</strong>ard deviation <strong>of</strong> <strong>the</strong><br />

annual cont<strong>in</strong>uously compounded growth <strong>rate</strong> was 11%. Assum<strong>in</strong>g <strong>the</strong> dividend growth <strong>rate</strong>s are lognormally distributed<br />

� 0.5�<br />

<strong>the</strong> expected annual dividend growth <strong>rate</strong> is e �<br />

where � is <strong>the</strong> expected annual cont<strong>in</strong>uously compounded growth <strong>rate</strong><br />

2<br />

<strong>and</strong> � is <strong>the</strong> variance <strong>of</strong> <strong>the</strong> annual cont<strong>in</strong>uously compounded growth <strong>rate</strong>.<br />

Competition Economists Group<br />

www.CEG-AP.COM<br />

2<br />

64 The longest published series by <strong>the</strong> Bureau <strong>of</strong> Economic Analysis at <strong>the</strong> US Department <strong>of</strong> Commerce<br />

http://www.bea.gov/national/<strong>in</strong>dex.htm#gdp.<br />

51

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