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# variance

1. ### P1.T2.20.11. Sample moments and bias

Learning objectives: Estimate the mean, variance, and standard deviation using sample data. Explain the difference between a population moment and a sample moment. Distinguish between an estimator and an estimate. Describe the bias of an estimator and explain what the bias measures. Questions...
2. ### P1.T2.20.10. Conditional expectations and the i.i.d. property

Learning objectives: Compute the variance of a weighted sum of two random variables. Compute the conditional expectation of a component of a bivariate random variable. Describe the features of an iid sequence of random variables. Explain how the iid property is helpful in computing the mean and...
3. ### P1.T4.921. Risk contribution toward the portfolio's unexpected loss (Schroeck Ch.5)

Learning objectives: Define and calculate expected loss (EL). Define and calculate unexpected loss (UL). Estimate the variance of default probability assuming a binomial distribution. Calculate UL for a portfolio and the UL contribution of each asset. Questions: 921.1. The following simplified...
4. ### YouTube T2-25: Comparing volatility approaches: MA versus EWMA versus GARCH

The general form for all three is: σ^2(n) = γ*V(L) + α*u^2(n-1) + σ^2(n-1).
5. ### YouTube T2-23: Volatility: GARCH 1,1

The GARCH(1,1) volatility estimate shares a similarity to EWMA volatility: both assign greater (lesser) weight to recent (distant) returns. But the GARCH(1,1) has an additional feature: it models a long-run (aka, unconditional) variance toward which the volatility series is pulled. David's XLS...
6. ### New to the Forum - simple variance question

How is the variance calculated? I'm sort of stuck on this problem, although I was able to understand it during the 6-sided die example. Thanks for any help!
7. ### Inconsistent Scaling in VaR/Standard Deviation for 2+ Assets/Portfolio

I've noticed that when calculating VaR/variance/std. dev of 2+ assets (or portfolio), sometimes the correlation/covariance is included, and sometimes it's not. I.e. for standard deviation of 2 assets: sqrt[w(1)^2*variance(1) + w(2)^2*variance(2)+2*w(1)*w(2)+covariance(1,2)] where (1) = asset 1...
8. ### YouTube T2-5 Variance of a discrete random variable

The variance is a key measure of dispersion, it is the expected value of the squared difference between each value and the mean. The population variance is the "true" variance, but realistically in most cases, we have a sample (rather than a population) such that our unbiased estimate of the...
9. ### P1.T2.712. Skew, kurtosis, coskew and cokurtosis (Miller, Chapter 3)

Learning objectives: Describe the four central moments of a statistical variable or distribution: mean, variance, skewness, and kurtosis. Interpret the skewness and kurtosis of a statistical distribution, and interpret the concepts of coskewness and cokurtosis. Describe and interpret the best...
10. ### P1.T2.711. Covariance and correlation (Miller, Ch.3)

Learning objectives: Calculate and interpret the covariance and correlation between two random variables. Calculate the mean and variance of sums of variables. Questions: 711.1. The following probability matrix displays joint probabilities for an inflation outcome, I = {2, 3, or 4}, and an...
11. ### P1.T2.710. Mean and standard deviation (Miller, Ch.3)

Learning objectives: Interpret and apply the mean, standard deviation, and variance of a random variable. Calculate the mean, standard deviation, and variance of a discrete random variable. Interpret and calculate the expected value of a discrete random variable. Questions: 710.1. The...