The trade off all investing is built on

Bill Sharpe is considered one of the great thinkers about investment markets, a Nobel Prize in Economics winner (1990) for his part in the research behind the capital asset pricing model, a model that helped describe the profound investment link between risk and return.
By · 13 Nov 2023
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13 Nov 2023 · 5 min read
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He also has a key financial measure, the Sharpe ratio, named after him. The Sharpe ratio compares the excess return on an investment with the volatility of an investment – a way of looking at the link between return and volatility.

The Profound Relationship Between Risk and Return

The capital asset pricing model and the Sharpe ratio were both a product of the 1960’s, with a focus on the relationship between investment risk and return. While investment risk can be described in different ways, in terms of owning shares it is often talked about in terms of volatility.  Cash, comparatively, is a less volatile investment – it has known and steady returns. Shares, on the other hand, will have periods of above average returns and, as we are seeing now, periods when they fall in value.

An Example of the Risk – Return Trade-off

This trade-off between risk and return is not just theoretical, it is possible to observe it in real life.  Let’s consider 3 different portfolios:

1 Portfolio is 100% cash

1 Portfolio is 50% cash and 50% shares (a balanced-style portfolio)

1 Portfolio is 100% shares

By looking at these three portfolios where the cash rate is 5%, and the return from shares varies from 25% (good year) to 10% (average year) and -5% (poor year), we can see the way returns are linked to the amount of risk, in this case exposure to shares, taken on by the portfolio.

In the table below, we have used the spread of returns as a measure of the volatility of a portfolio.

Table 1: Theoretical Portfolio Returns for Portfolios with Varying Asset Allocations


Return in a Good Year

Cash = 5%

Shares = 25%

Return in an Average Year

Cash = 5%

Shares = 10%

Return in a Poor Year

Cash = 5%

Shares = -5%

Spread of Returns

100% cash

5% return

5% return

5% return


50% cash

50% shares

(Balanced Portfolio)

15% return

7.5% return

0% return


100% shares

25% return

10% return

-5% return


200% shares

-100% cash (borrowing at 7%)



42.5% return



12.5% return



-17.5% return




We can also create a 4th portfolio, one that has doubled their portfolio by borrowing (ie a $10,000 portfolio borrows another $10,000 to give $20,000 worth of market exposure) at the rate of 7.5% (a margin above the cash rate).  This increases the possible return of the portfolio – in a ‘normal’ year a 10% return from shares becomes a 12.5% return (10% x 2 -7.5% borrowing cost) for the portfolio, while also increasing the volatility of returns – the 25% share return in a good years becomes and exciting 42.5% return, and the -5% return in a poor year becomes a -17.5% return for the portfolio after the poor return and interest costs are taken into account.

The Impact of Fees for Investors

If this profound investment relationship holds – that there is a trade-off between risk and return with higher returns requiring an investor to take on higher risk – it starts to become evident that the fees we pay as investors are crucial, because if we pay too much in fees, that will decrease the returns of a portfolio while keeping the spread of returns the same.

Consider our ‘balanced’ share portfolio.  A fee of 0.5% per annum across the portfolio will see a return of 14.5% after fees in a good year, 7% after fees in an average year and -0.5% per year in a poor year.  The spread of returns stays the same (15%), but the return in each situation is reduced.  This is not a huge deal with a 0.5% fee, but with a 2% fee – and there are plenty of fund managers charging 2% for a balanced fund – and it becomes more significant. 

Bill Sharpe’s Contributions on the Subject

This brings us very nicely to two important contributions that Bill Sharpe has made in discussing fees.  The first one is a theoretical discussion of market returns, from an article titled, ‘The Arithmetic of Active Management’.  He splits the overall sharemarket into two parts, those who use an index approach (the minority of the market), and those who are active.  Let’s say the overall average return from the market is 10%. 

Those using an index approach will receive a return of 10%, less the small fees from an index/ETF style investment.

The remaining average on the active part of the market must also be 10%.  However, this is the part of the market where people have spent more money to invest – paying more for research, fund managers and more regular trading.  Sharpe explains:

"Because active and passive (index style) returns are equal before cost, and because active managers bear greater costs, it follows that the after-cost return from active management must be lower than that from passive management."

Later in the article he restates this finding:

"To repeat: Properly measured, the average actively managed dollar must underperform the average passively (index) managed dollar, after costs. Empirical analyses that appear to refute this principle are guilty of improper measurement."

A second contribution, around the impact of investment fees, contains valuable information. From the 2013 paper titled, ‘The Arithmetic of Investment Returns’ (Link: The Arithmetic of Investment Expenses by William F. Sharpe :: SSRN), he found choosing a low fee investment option could produce a 20% higher standard of living for investors in retirement. 

It is interesting to see someone whose life has been involved in the theoretical analysis of investment returns, starting back in the 1960’s with CAPM and the Sharpe ratio, turning his mind to the very real challenge of a retirement ‘standard of living’.


There is a fascinating journey of Bill Sharpe’s work, starting with the consideration of the relationship between risk and return in investments, and finishing with important contributions around the impact that fees play on investment returns and, ultimately, the standard of living we experience in retirement. If there is a relationship between risk and return from investing, and many would describe that as THE profound investment relationship, then in pays to ensure that your investment fees are modest.

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