Table of Contents

## What are the 3 primary yield curve reshaping movements measured by the 3 principal components?

movements of the yield curve in terms of three main factors: level, slope, and curvature.

### What is the value of PCA?

The VFs values which are greater than 0.75 (> 0.75) is considered as “strong”, the values range from 0.50-0.75 (0.50 ≥ factor loading ≥ 0.75) is considered as “moderate”, and the values range from 0.30-0.49 (0.30 ≥ factor loading ≥ 0.49) is considered as “weak” factor loadings.

#### What does a PCA analysis tell you?

Principal component analysis, or PCA, is a statistical procedure that allows you to summarize the information content in large data tables by means of a smaller set of “summary indices” that can be more easily visualized and analyzed.

**How do you interpret a PCA plot?**

Use the loading plot to identify which variables have the largest effect on each component. Loadings can range from -1 to 1. Loadings close to -1 or 1 indicate that the variable strongly influences the component. Loadings close to 0 indicate that the variable has a weak influence on the component.

**What’s the riskiest part of the yield curve?**

What’s the riskiest part of the yield curve? In a normal distribution, the end of the yield curve tends to be the most risky because a small movement in short term years will compound into a larger movement in the long term yields. Long term bonds are very sensitive to rate changes.

## What are the three main theories that attempt to explain the yield curve?

Three economic theories—the expectations, liquidity-preference, and institutional or hedging pressure theories—explain the shape of the yield curve.

### How is PCA calculated?

Mathematics Behind PCA

- Take the whole dataset consisting of d+1 dimensions and ignore the labels such that our new dataset becomes d dimensional.
- Compute the mean for every dimension of the whole dataset.
- Compute the covariance matrix of the whole dataset.
- Compute eigenvectors and the corresponding eigenvalues.

#### What is PCA example?

Principal Component Analysis, or PCA, is a dimensionality-reduction method that is often used to reduce the dimensionality of large data sets, by transforming a large set of variables into a smaller one that still contains most of the information in the large set.

**What is PCA good for?**

PCA helps you interpret your data, but it will not always find the important patterns. Principal component analysis (PCA) simplifies the complexity in high-dimensional data while retaining trends and patterns. It does this by transforming the data into fewer dimensions, which act as summaries of features.

**What do PCA loadings mean?**

PCA loadings are the coefficients of the linear combination of the original variables from which the principal components (PCs) are constructed.

## Why do stocks go down when bond yields rise?

The yield on bonds is normally used as the risk-free rate when calculating cost of capital. When bond yields go up then the cost of capital goes up. That means that future cash flows get discounted at a higher rate. This compresses the valuations of these stocks.

### What are the three types of yield curves?

There are three main shapes of yield curve shapes: normal (upward sloping curve), inverted (downward sloping curve), and flat.

#### What are four types of yield curve?

There are four classifications of yield curves depending on their shape: the normal yield curve, the steep yield curve, the flat yield curve, and the inverted yield curve.

**When should you use PCA?**

PCA should be used mainly for variables which are strongly correlated. If the relationship is weak between variables, PCA does not work well to reduce data. Refer to the correlation matrix to determine. In general, if most of the correlation coefficients are smaller than 0.3, PCA will not help.

**How do we calculate PCA?**

## What are the pros and cons of PCA?

What are the Pros and cons of the PCA?

- Removes Correlated Features:
- Improves Algorithm Performance:
- Reduces Overfitting:
- Improves Visualization:
- Independent variables become less interpretable:
- Data standardization is must before PCA:
- Information Loss:

### What is the disadvantage of using PCA?

PCA assumes a linear relationship between features. The algorithm is not well suited to capturing non-linear relationships. That’s why it’s advised to turn non-linear features or relationships between features into linear, using the standard methods such as log transforms.

#### How do you interpret PCA loading values?

Positive loadings indicate a variable and a principal component are positively correlated: an increase in one results in an increase in the other. Negative loadings indicate a negative correlation. Large (either positive or negative) loadings indicate that a variable has a strong effect on that principal component.

**What are the best books on relative value trading?**

Salomon Smith Barney, (2000), “Principles of Principal Components: A fresh look at Risk, Hedging, and Relative Value”. Standard Chartered (2013), “Introducing a relative value tool for swaps”. TD Securities (2015), “Market Musings — Relative Value Across the U.S. Swap Surface: A PCA Approach”.

**What is arbitrage in the hedge fund World?**

But in the hedge fund world, arbitrage more commonly refers to the simultaneous purchase and sale of two similar securities whose prices, in the opinion of the trader, are not in sync with what the trader believes to be their “true value.”

## Which stocks are best for relative-value arbitrage?

Stocks in the same industry that have trading histories of similar lengths are often used in relative-value arbitrage. Automotive stocks GM and Ford are good examples, as are pharmaceutical stocks Wyeth and Pfizer. But indices, such as the S&P 500 Index and the Dow Jones Utilities Average, can also be used in relative-value arbitrage.