# fund manager efficiency

efficiency = skill * breath * implementation

IR = IC * sqrt(N) * TC

There is this great paper talking about a key measurement named information ratio – which is the excess return for a unit of active tracking error [JPMorgan]. Keep in mind that it is different from the Sharpe ratio as the information ratio is related to the excess return and risk with respect to an existing benchmark, so instead of the absolute volatility, it will be the tracking error.

At a very high level, IC is the information coefficient between -1 and 1 that indicates how good a manager expect to be and turn out to be. The information ratio also grow with the number of independent decisions and the last item, transfer coefficient means the level of constraint.

If you are particular interested in information coefficient on its own, this is an video from Quantopian teaching you how it is being measured from the practical point of view.

# Shift, Twist & Curvature to explain all yield curve changes

Yield curve change is referring to as time passes, how the different yield changes for different maturity. Rather than calculate the difference for each single maturity, industry has always been seeking a way to simplify the and find a simple explanation. And the three key components behind any yield curve change is the famous shift, twist and curvature.

Just like you can use x, and y to explain all the positions on a 2D space, you can use shift twist and curvature to explain all the yield curve changes. These three components are also constructed as uncorrelated factors.

There is this great youtube video that further explained how the three components are being calculated using Principal Component Analysis.

Once we understand that three components of changes, the next step is usually to prepare the actions in anticipation of changes in each component. For example, if you have three different options of structuring your portfolio as laddered, barbell or bullet.

Then you can use them to list all the possible combinations of three factors, and calculate the potential outcomes.

You can weight the different scenarios differently based on your own forecast of the yield curve and use the probability weighted average as the expectation to pick the best action item.

Exhibit 76, and Exhibit 77 are screenshots from the CFA Curriculum and copyright reserved to them.

# Riding/Rolling Down the Yield Curve

Yield curve is the a graph that demonstrates the relationship between yield (say government bond) versus different maturity. Just like you purchase CD, that they offer 1% interest rate for 1 year, and 3% for 10 year. A yield curve in most of the time is a upward sloping curve.

The fund part is that the yield curve is only a snapshot. It means that as time passes by, the government might issue new bonds with a different interest rate/yield for the same maturity, and this change can happen to short term bond, medium term or even long term bond. And the next snapshot might look very differently. When the shape changes, the bond that you are holding will still have the same future nominal cashflow but the real value of your bonds will have immediate capital gain when the yield drops or suffer losses when the yield raises.

Assuming that the yield shape will stay fairly static, there is a fixed income technique called rolling down the yield curve / ride the yield curve to enhance the return. The return is as high as the coupon rate, but you can achieve capital gain if you buy at a long term but sell as short term.

When you discount the future cashflows that priced via a long term, the market yield for short term bonds tend to be the low, and if you discount using a lower discount rate, the valuation of your bond will be higher.

Here I listed a 10 year bond with a 5% yield that originally priced at par. Assuming that at the end of the every year, we will consider selling it and the yield for the rest of the maturity will be proportionally decreasing. For example, if you sell at end of year one. Your bond become a 9 year bond and will be valued with the yield that is 4.5%, rather than 5, so on and so forth. As you can tell, the present value of the bond varies based on the yield curve and we happen to have a peak point to maximize the capital gain.

In this particular example, the best decision is actually to sell the bond end of year 1 to maximize the annual gain.

Let’s take a look at another yield curve shape. If we change the yield curve to be concave, we can actually find that the annual income is maximize if we sell at year 6.

If the yield curve is convex. This is how it looks like.