# Units of Exchange

There was a period not so long ago on a planet not so far when I lost all concept of value.

I had lived in many countries in as many months and lost track of what anything was worth.

Euros, USD, SGD, IDR and AUD became indistinguishable units of exchange, a means to an end, I handed over a fist of cash for whatever was required.

You can perhaps overlook day to day expenses, but of course there are times when a lot is riding on an exchange.

You need an accurate unit to compare relative value.

Currency is one way to value things as long as the objects of desire are relatively homogenous.

However, if a currency's value wobbles erratically due to inflation, the lack of the *currency's* homogeneity over time will lead people to vote with their wallets and adopt another steadier denomination. Usually USD.

#### Bonds

There are other units of value used in finance.

Bond markets use par yields rather than units of currency. The issue with bond prices is that bond's coupons and principals are heterogeneous and yields provide a quick shorthand to make comparisons.

Of course if you compare bonds with different maturities you run into a problem again.

For example, pitching me a 10 year zero coupon bond with a yield of 10% is a very different proposition to one maturing in a year with 10% yield.

We should earn 10% per annum on each, but one keeps our capital tied up over a full ten years. The opportunity cost is less with the yearly bond, it is the cheaper bond, and probably riskier.

Corporate yields can however be broken into the yield apportionable to the current prevailing interest rate and the credit spread for that specific issuer or company.

Indeed if we found the credit spreads for both bonds in our example we would find the one year bond was wider than the ten year bond.

Finding concise ways to compare assets get us to the core of the asset, i.e. the creditworthiness of the issuer is the chief determinant of acorporate bond's relative value.

#### Options

In a similar way, options are valued using implied volatility as a shorthand which *tries* to cut to the chase.

Implied volatilities are often not sufficient to fully compare options, because of implied skewness, embodied in the CBOE's Skew index.

#### Portfolios

As complexity increases so does the difficulty in making comparisons. Hundreds of analytics can be used to compare two portfolios, there is no silver bullet.

One of the most popular ways however is using the Sharpe ratio.

One issue with the Sharpe ratio is comparing ratios found over different time periods.

For example a strategy with an annualised Sharpe of 2 backtested over 2 years has a one in ten chance of being profitable.

However, a much lower Sharpe of 0.25 accrued over 25 years of backtesting will have the same probability of ending in the black!

These probabilities are a accurate way of comparing Sharpes, but part of the enduring appeal of the ratio is seeing bang for the buck - or dollar return per dollar standard deviation at risk.

So how about standardising and rebasing everything to a 10 year backtest period?

The 'War of Ideas' strategy was backtested over 10 years and had a Sharpe of 0.833 or 1.36% chance of trading noise.

The latest 'Skewerage' strategy accrued a Sharpe of 0.67 over 25 years or about a 0.13% chance that we're trading noise. Clearly 0.67 over 25 years is a far better result than 0.833 over 10.

In fact in 10 year terms it is equivalent to 1.3.

The 'Steady Vol' Sharpe of 0.56 over 25 years turns into 1.01 over 10 years.

The spreadsheet formula to convert a Sharpe into a probability is:

`=tdist(sharpe*sqrt(years),years-1,1)`

so for the latest 'Dawn of Justice' strategy for example

`=tdist(0.865*sqrt(25),25-1,1)`

is 0.01%.

The conversion to a ten year Sharpe is:

`=-T.INV(probability,years-1)/sqrt(years)`

or

`=-T.INV(0.0001,10-1)/sqrt(10)`

which is 1.86.

#### Conclusion

It seems only fair Sharpes from longer more rigorous testing should be compensated; and therefore sensible to compare like with like.

Coming up with an accurate way to compare also gets to the core of what we are really searching for - more reliable performance.