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8
votes
2answers
369 views

GARCH model, expectation of volatility?

Consider a time series $\{r_t\}$ following a standard GARCH(1,1) model, i.e., $$ r_t = \sigma_t \epsilon_t,$$ where $\epsilon_t \sim N(0,1)$ and are i.i.d, and $$\sigma_t^2 = \omega + \alpha_1 ...
1
vote
2answers
96 views

Modern portfolio theory in practice

I am wondering about the Markowitz theory of portfolio construction in practice. Hence, if one wants to know the efficient frontier, what variances can one use. The only method that I can think is the ...
0
votes
0answers
27 views

scale alpha forecasts to align with covariance matrix

I have a set of monthly alpha forecasts and my covariance matrix has been annualized. I would like to do a mean variance optimization with a linear tcost penalty term. How do I rescale my alpha ...
2
votes
1answer
55 views

What is the relationship between arithmetic versus geometric averages and simple versus logarithmic prices?

I know that the geometric mean is used in order to make percentage returns across time comparable. Similarly, I know that log prices make percentage returns comparable for example when prices are ...
1
vote
2answers
2k views

Sharpe Ratio, annualized monthly returns vs annual returns vs annual rolling returns?

I would like to calculate the Yearly Sharpe Ratio on MSCI World index I have monthly values of the index that falls back up to Jan/1970, hence about: 44 years, 528 months In order to calculate ...
0
votes
1answer
183 views

Calculating the Sum of Squared Deviations between two Normalized Price Series

How can I calculate the sum of square deviations between two normalized price series according to (Gatev et. co 2006)? My normalized price series of stocks $X$ and $Y$ consist of the cumulative total ...
0
votes
0answers
78 views

Mean-variance minimizser

I am working on a project that involves pricing european call options in incomplete markets. Now I need to find a unique measure $Q^*$ such that $$Q^* = \min_{M_e} E_Q [V(T)-F(w)]^2 = \min_{u} E_Q ...
8
votes
3answers
4k views

R code for Ornstein-Uhlenbeck process

Can any one help me with some R code to run Ornstein-Uhlenbeck process?
5
votes
1answer
2k views

Mean Reversion Time Frame

I am running a mean reversion strategy. I have question with regards to half-life; I have heard of OU process to determine the high life but it's not giving me the kind of result. Can any one ...
4
votes
3answers
2k views

Mean reverting Indicator

I'm looking for an indicator which tells me if it's a good time to use mean reverting type quantitative trading strategies. In order to do so I look at the market (the few hundred stocks I trade) and ...