Return characteristics Flashcards
What are simple returns?
Simple returns are the percentage changes in prices between to periods.
Rt = (Pt - Pt-1) / Pt-1
What is the formula for simple returns over n periods?
Rt = (Pt / Pt-n) - 1
What are continuously compounded returns?
Continuously compounded returns are defined as the logarithm of gross return.
Yt = ln(1 + Rt)
What is the formula for continuously compounded returns over n periods?
Yt(n) = ln(1 + Rt(n)) Yt(n) = Yt + Yt-1 + ... + Yt-n+1
What are the advantages of continuously compounded returns?
When calculating over n periods the CCR’s are just the sum of the periods. They also have the property that they are symmetric. This is useful many financial calculations.
What are the disadvantages of continuously compounded returns?
Strictly speaking they are not correct. They differ somewhat from simple returns. Another disadvantage is that portfolio returns cannot be calculated as a weighted average of the returns of individual assets, as is the case with simple returns.
When, or under what conditions, are continuously compounded returns equivalent to simple returns?
Only if the time between observations goes to zero.
What are the three main stylized facts of financial returns?
Volatility clusters,
Fat tails,
Nonlinear dependence.
How can the presence of volatility clusters be identified?
Volatility clusters means that the squared returns have autocorrelation structures. This means that to detect volatility clusters one can detect the autocorrelation patterns. This can be done by Ljung-Box tests or plotting the autocorrelation function of the squared returns.
What are fat tails?
A distribution has fat tails if it has a higher chance of extreme outcomes than the normal distribution with same mean and variance. This also means the distribution is more flat, and thus non-extreme outcomes are less likely.
What graphical method can be used to detect fat tails? Explain this method.
A QQ-plot, where the quantiles of the target distribution are compared to those of the normal distribution. There are fat tails if there are more observations on the high end, and less on the low end as compared to the normal distribution.
What are the financial implications of fat tails?
When one assumes returns to be normally distributed, extreme cases and thus risk of the investment is underestimated.
