Questions tagged [mean]
The mean tag has no usage guidance.
34 questions
3
votes
0
answers
120
views
Shrinkage estimators outside MVO? Sample mean or James-Stein estimator?
Generic question: Are there any uses of Shrinkage estimators, such as James-Stein estimator for mean or Ledoit-Wolf estimator for covariance matrix outside mean-variance optimization (MVO) framework? ...
- 692
0
votes
1
answer
124
views
Monthly and annual arithmetic mean in valuations? [closed]
I know this is back to basics but I am perplexed by it!!!
Assume that the future value (FV) of an investment at the end of year 1 is 112, the annual arithmetic expected return is 12%, hence the ...
- 61
1
vote
0
answers
91
views
How much compensation need to take on risk?
Quant Firm Interview Question
We roll three, 8 sided dice. If same face appears 3 times we win 80 dollars. We have a bank of 10,000 dollars. How much are we willing to pay to play? What if we increase ...
- 83
0
votes
1
answer
100
views
Verify numerically relation between mean deviation and standard deviation
I was reading "We Don’t Quite Know What We Are Talking About When We Talk About Volatility" by Goldstein and Taleb, and I was trying to quickly verify numerically the relation between mean ...
1
vote
0
answers
57
views
Time step in Hull white mean reverting model
Specially for mean reverting processes for interest rate simulation. Is it acceptable to directly simulate the paths at say 1 month horizon without stepping through time? Please advice.
- 11
3
votes
1
answer
2k
views
How to properly calculate the average across multiple correlations?
I'm trying to obtain an average across 3 correlations.
Using Python, I obtain these correlations with:
corr = df.apply(lambda s: df.corrwith(s))
which outputs:
<...
- 125
1
vote
3
answers
10k
views
What is better: A negatively skewed return or a positively skewed returns distribution?
I noticed that in certain literature, like in CFA level 1, the theory put forth is that someone should prefer positively skewed returns as mean > median > mode. But why is that?
Based on a ...
- 155
0
votes
1
answer
202
views
Mean estimate in portfolio optimization (Markowitz) [duplicate]
The Markowitz mean-variance portfolio optimization problem is to find the optimal allocation, $w_{optimal}$ by solving:
\begin{equation}
w = \mathrm{argmax} \ \mu_{t}^Tw - \frac{\gamma}{2}w^{T}\...
- 11
12
votes
9
answers
3k
views
Why is asset volatility easier to estimate than the asset mean if it contains the mean?
It is well known that the variance of asset returns, $\sigma^2$ (whose square root is volatility), is easier to estimate than the asset mean $\mu$ (also known as expected return) because the mean of ...
- 3,090
1
vote
1
answer
54
views
How to evaluate prediction(s) made of the asset return mean?
In finance, it is well-known that the expected value of asset returns, $\mu$, otherwise known as the average return or mean or first statistical moment, is difficult to predict. I think it was ...
- 3,090
0
votes
1
answer
165
views
the relationship between VaR(0.05) and mean?
What is the meaning of the difference between the quantile of prob=0.05 and mean for a sample form a specific distribution?
In other words, I would like to understand the relationship between ...
- 1
1
vote
1
answer
116
views
arithmetic mean of log returns that starts and ends with the same price in a time series
quick question:
arithmetic mean of log returns that starts and ends with the same price in a time series
say a stock time series starts at t0 price 100 fluctuates in between the time series and ends ...
- 111
2
votes
1
answer
73
views
ARMA moments proof
Consider a standard ARMA(1,1) process such as
$$x_t - \beta x_{t-1} = \theta u_{t-1} + u_t$$
where $u_t$ is i.i.d. $u_t \sim N(0,\sigma^2)$. I know how to derive mean and variance with stationary ...
- 133
11
votes
2
answers
10k
views
Returns and logreturns differences
I have a time series of stock prices and I tried to calculate simple returns and log returns. However, I end up that simple returns has positive mean, but log returns has negative mean. Is it possible ...
- 133
1
vote
0
answers
20
views
Average interest rate [duplicate]
Earlier I asked a question about average FX rate. I'm building simple linear model and need to use monthly data. I have a yearly interest rate that changes daily. How to aggregate it over the month, ...
- 85
0
votes
0
answers
80
views
Currency exchange rate
I'm working with monthly data and I need to use FX rate in my model. I have daily data for exchange rate and not sure how to average it over the month. Should I compute simple arithmetic average over ...
- 85
0
votes
0
answers
115
views
mean reversion model estimation - what method?
how can I estimate this model for mean reversion?
0
votes
1
answer
1k
views
Vasicek model and spot interest rate parametrised by reversion rate
By solving an SDE I want to derive the analytical results for mean and variance of the process of extended Vasicek model.
$$
dr(t) = \left(\eta - \gamma r(t) \right)dt + c dX(t)
$$
where $\gamma$ ...
3
votes
1
answer
416
views
What is the correct way to calculate the annualized returns from rolling windows starting from monthly returns?
What is the correct way to calculate the annualized returns in 5-year rolling estimation windows starting from monthly returns?
Is it most correct to first annualize the returns (using the geometric ...
- 153
4
votes
1
answer
483
views
Portfolio diversification and Sharpe ratio
I have a given trading strategy T and say 3 assets in my universe. The hold time is one day. The trading strategy can general signals for the 3 assets in any given day (so signal can trigger for any ...
- 141
2
votes
2
answers
87
views
Why can we neglect the mean in the variance when the time step is very small?
Can anyone tell me why we can neglect the mean in the variance when the time step is very small? See the following picture:
Usually, we choose a time step of one day. Is it small enough?
- 1,253
1
vote
0
answers
187
views
Interpretation of Skew and Kurtoisis - strategy backtesting
I am working on my dissertation and i would like to provide a nice interpretation of two tables which i will present below.
I have 10 portfolio buckets which i sort on 6 different attributes. One of ...
- 210
0
votes
1
answer
661
views
GARCH Model Constant in Regression
When regressing a variable on a constant of 1, the coefficient of this constant is the mean. However, when I specified that the residuals follow a GARCH(1,1) model, the coefficient of the constant ...
- 221
1
vote
1
answer
1k
views
One-step ahead forecast of a AR(1) process (GARCH context)
I am using a Matlab toolbox for obtaining one-step ahead forecasts of the conditional mean from the ARMA(1,0)-GARCH(1,1) process and I have encountered a piece of code that contains, in my opinion, a ...
- 491
3
votes
0
answers
494
views
Finding mean vector and covariance matrix for annual returns given quarterly returns
I am currently trying to calculate a vector for the mean annual returns of 4 different asset classes along with their 4x4 covariance matrix in excel. However, I am having problems since the data I ...
- 31
12
votes
2
answers
1k
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
$$\sigma_t^2 = \omega + \alpha_1 r_{t-1}^...
- 121
1
vote
2
answers
506
views
Modern portfolio theory in practice
I am wondering about the Markowitz theory of portfolio construction in practice. Hence, if one wants to know the efficient frontier, what variances can one use. The only method that I can think is the ...
- 59
3
votes
1
answer
353
views
What is the relationship between arithmetic versus geometric averages and simple versus logarithmic prices?
I know that the geometric mean is used in order to make percentage returns across time comparable. Similarly, I know that log prices make percentage returns comparable for example when prices are ...
- 622
4
votes
2
answers
14k
views
Sharpe Ratio, annualized monthly returns vs annual returns vs annual rolling returns?
I would like to calculate the Yearly Sharpe Ratio on MSCI World index
I have monthly values of the index that falls back up to Jan/1970, hence about: 44 years, 528 months
In order to calculate ...
- 406
0
votes
1
answer
1k
views
Calculating the Sum of Squared Deviations between two Normalized Price Series
How can I calculate the sum of square deviations between two normalized price series according to (Gatev et. co 2006)? My normalized price series of stocks $X$ and $Y$ consist of the cumulative total ...
- 163
2
votes
0
answers
91
views
Mean-variance minimizser
I am working on a project that involves pricing european call options in incomplete markets. Now I need to find a unique measure $Q^*$ such that
$$Q^* = \min_{M_e} E_Q [V(T)-F(w)]^2 = \min_{u} E_Q [V(...
- 41
23
votes
2
answers
2k
views
Diversification, Rebalancing and Different Means
I have found many financial authors making generalizations about the geometric mean (GM) and arithmetic mean (AM) but they are wrong in certain circumstances. Could someone explain their reasoning?
My ...
- 705
18
votes
4
answers
14k
views
R code for Ornstein-Uhlenbeck process
Can any one help me with some R code to run Ornstein-Uhlenbeck process?
- 1,397
3
votes
3
answers
5k
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 ...
- 2,303