1. Exploring other kinds of risk factors
I hope you are now getting the hang of how to explore the risk-factor time series.
2. Exploring other kinds of risk factors
In particular, you should be comfortable with calculating log-returns, which are the main kinds of data we model in market-risk applications of quantitative risk management. And you should be comfortable with aggregating log-returns by summing them to obtain longer-interval log-returns. For example, aggregating daily log-returns to obtain weekly, monthly, and quarterly log-returns.
So far, you have looked at equity data, both indexes and individual stocks, and you have looked at foreign-exchange or FX data.
To conclude the first chapter, you are going to look at two other kinds of data: commodities prices and zero-coupon bond yields.
3. Commodities data and interest-rate data
First commodities data. Imagine you invest in gold or oil. How do the price risk factors for these commodities behave? Are they similar to stocks, or are there differences?
Now suppose you invest in fixed-income securities like government bonds or treasuries.
The simplest kind of bond to analyze is called a zero-coupon bond. This is a bond that pays a fixed amount at a future time known as the maturity, but which pays no intermediate interest income.
4. Bond prices
Let p(t,T) denote the price at time small t of a zero-coupon bond paying one unit at time capital T.
Big T is the maturity of the bond. That is the time at which the bond investor gets their money back.
p(0, 10) is the price at time 0 of a bond maturing in 10 years, or 10-year bond.
p(0, 5) is the price at time 0 of a 5-year bond.
p(5, 10) is the price of a 10-year bond after five years.
5. Yields as risk factors
Rather than taking the price of the zero-coupon bond as a risk factor, it is quite common to take the risk-factor to be the so-called yield.
The yield y(t, T) is defined by the simple equation given on the slide. It is a measure of the rate of return per unit of time.
y(t, 10) gives the yield for an investor who buys a 10-year bond at time t. y(t, 5) is the yield for an investor who buys a 5-year bond at time t.
The main reason yields are preferred to prices is that they are comparable across different maturities T. You can directly compare the rates of return for investors who invest in 5-year bonds and 10-year bonds by comparing their yields y(t,5) and y(t,10).
The set of yields y(t,T) for fixed small t and varying capital T is known as the yield curve at time t and is said to describe the term structure of interest rates.
If you take the risk factors to be yields, there is a question about whether you should analyze log-returns or simple returns of yields. In a low-interest-rate environment and an environment where rates can become negative, there are arguments for using simple returns.
6. Let's practice!
So now you are going to try out some exercises on commodities and bond yields.