Empirical asset pricing with Tidy Finance

class: center, middle, inverse, title-slide

.title[
# Empirical asset pricing with Tidy Finance
]
.subtitle[
## www.tidy-finance.org
]
.author[
### Patrick Weiss
]
.date[
### March 19, 2024
]

---

class: chapter-slide

# Talk outline

---
## What is this talk about?

1. Career paths in **Finance** and **academia**

2. Open-source project **Tidy Finance**

3. **Empirical asset pricing**

---
class: chapter-slide

# Finance and academia

---
## My own journey

- Raised and socialized in Vienna, Austria

- *My plan:*
  + Undergraduate business degree with a focus on management
  + Add an international master's program in management
  + Become an important manager, get rich, and have a family

- **The reality:**
  + Switch during undergraduate degree to focus on finance and mathematics
  + Stay in Vienna to complete a **quantitative finance** program
  + Complete the **CFA charter** to push industry career prospects
  + Then, continue directly with a **PhD in Finance**

---
## Today's view on Patrick Weiss

&nbsp;

.pull-left[
<middle><center><img style="border-radius: 50%;" alt="Portrait of Patrick Weiss" src="images/pic_patrick.jpg" width="200px"/></center></middle>

.center[**Patrick Weiss**

- External lecturer at WU Vienna

- Research focus on empirical asset pricing with equities and bonds

- Published in top finance journals

- Co-author of Tidy Finance (two textbooks)
]

---
## What do I take away from my journey?

- A simplified version: *You never know what life has to offer*? - No.

- My main problem with *management* was (is) the **lack of quantifiable relations** for decision making.
  + Good leaders are absolutely important.
  + However, we hardly know what makes a good manager nor how to learn the craft.
  
- What drew me to finance is the hope of making informed decisions.
  + The person with the **right analysis wins** (also against their boss).
  + Put differently: Truth trumps anything.
  + At the heart, any decision can be mapped to a **financial decision**.

- The core ideas of finance and academia seem optimal to me.

---
class: chapter-slide

# Tidy Finance

---
### #TidyFinance is ...

.pull-left[
- ... an open-source project available at [tidy-finance.org](https://www.tidy-finance.org) and a published textbook.

- ... a step towards **reproducible finance** by providing a fully transparent code base.

- ... a resource for students, lecturers, and professionals using `R` for applications in finance.

- ... a **tidy** approach to finance.

- ... continuously maintained and expanded.
]

.pull-right[
<middle><center><img src="images/cover-book-r.jpg" alt="Cover image of 'Tidy Finance with R'. The figure reads Tidy Finance with R followed by the author's names; Christoph Scheuch, Stefan Voigt, and Patrick Weiss." width="350"/></center></middle>
]

---
class: middle

.pull-left[
### `R` is among the best choices for finance programming.

- Free, open-source software with a diverse, active **community**.

- Actively-maintained **packages** for all kinds of applications.

- Smooth integration with other **programming languages**.

- **RStudio** <svg aria-hidden="true" role="img" viewBox="0 0 512 512" style="height:1em;width:1em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:steelblue;overflow:visible;position:relative;"><path d="M225.8 468.2l-2.5-2.3L48.1 303.2C17.4 274.7 0 234.7 0 192.8v-3.3c0-70.4 50-130.8 119.2-144C158.6 37.9 198.9 47 231 69.6c9 6.4 17.4 13.8 25 22.3c4.2-4.8 8.7-9.2 13.5-13.3c3.7-3.2 7.5-6.2 11.5-9c0 0 0 0 0 0C313.1 47 353.4 37.9 392.8 45.4C462 58.6 512 119.1 512 189.5v3.3c0 41.9-17.4 81.9-48.1 110.4L288.7 465.9l-2.5 2.3c-8.2 7.6-19 11.9-30.2 11.9s-22-4.2-30.2-11.9zM239.1 145c-.4-.3-.7-.7-1-1.1l-17.8-20c0 0-.1-.1-.1-.1c0 0 0 0 0 0c-23.1-25.9-58-37.7-92-31.2C81.6 101.5 48 142.1 48 189.5v3.3c0 28.5 11.9 55.8 32.8 75.2L256 430.7 431.2 268c20.9-19.4 32.8-46.7 32.8-75.2v-3.3c0-47.3-33.6-88-80.1-96.9c-34-6.5-69 5.4-92 31.2c0 0 0 0-.1 .1s0 0-.1 .1l-17.8 20c-.3 .4-.7 .7-1 1.1c-4.5 4.5-10.6 7-16.9 7s-12.4-2.5-16.9-7z"></path></svg>
]

.pull-right[
### `{Tidyverse}` is the way for data analysis.

- Messy data cause pain. **Tidy data** cause joy.

- Compose simple functions with the **pipe**.

- Designed for **humans**.

- **Consistent** across packages.
]

---
### #TidyFinance goes Python

.pull-left[
- There is a **Python** version of Tidy Finance.

- It provides the same treatment of finance in Python as the previous book.

- Print release in **June 2024**.

- We also have a **blog** for external contributors.
]

.pull-right[
<middle><center><img src="images/cover-python.png" alt="Cover image of 'Tidy Finance with Python'." width="400"/></center></middle>

Check it out at [tidy-finance.org/python](https://www.tidy-finance.org/python/index.html)!
]

---
class: chapter-slide

# Empirical Asset Pricing

---
## Is empirical asset pricing important?

.pull-left[
- Asset prices are essential for efficient **resource allocation**.

- **Theoretical** insights have to be tested empirically.

- There are tons of **research articles** produced every year.

- Stock, bond, currency **markets** are enormous and affect our daily life.
]
.pull-right[
&nbsp;

<middle><center><img src="images/fearless_girl.jpg" alt="Image of a bronze statue of a girl in front of a statue of a bull." width="400"/></center></middle>
]

---
## Before we do anything else

- If you have not installation of `{tidyverse}`, run `install.packages("tidyverse")`

```r
library(tidyverse)
```

- It is the tool we use (and recommend) for data analysis in all contexts

---
## Where to get free data?

- There are several free financial data providers:
  + Yahoo!Finance
  + Kenneth French's website
  + FED & ECB data
  
- We will discuss how to access them and manipulate the data

- There are more free alternative presented in Chapter *Other data providers* of #TidyFinance

---
## Yahoo!Finance overview

- We start by downloading and visualizing stock data from Yahoo!Finance
  + Provides stock data for several frequencies
  + Adjusted prices for dividends & splits
  + Returns have to be computed from the price time series

- For this, we also load the convenient `{tidyquant}` package

```r
library(tidyquant)
```

---
## Apple stock data

- We retrieve stock market data for Apple (ticker AAPL) with `tq_get()`

```r
prices <- tq_get("AAPL",
  get = "stock.prices",
  from = "2000-01-01",
  to = "2021-12-31"
)
```

- `{tidyquant}` comes with additional features, but we will skip them here (consider `tq_index("DOW")` to get a set of tickers)

---
## Apple stock price (I)

- It is generally a good idea to look at your data, e.g., by visualizing it in a plot:

```r
prices |>
  ggplot(aes(x = date, y = adjusted)) +
  geom_line() +
  labs(
    x = NULL,
    y = NULL,
    title = "Apple stock prices between beginning of 2000 and end of 2021"
  )
```

---
## Apple stock price (II)

---
## Computing Apple's stock returns

- We can now compute stock returns from our prices
  + Considering adjusted stock prices (dividends and stock splits)
  + Returns can be computed as `$r_t = p_t / p_{t-1} - 1$`
  + Where `$p_t$` is the adjusted day `$t$` price

```r
returns <- prices |>
  arrange(date) |>
  mutate(ret = adjusted / lag(adjusted) - 1) |>
  select(symbol, date, ret) |> 
  drop_na(ret)
```

---
## Apple's stock returns: Historgram (I)

```r
quantile_05 <- quantile(returns |> pull(ret) * 100, probs = 0.05)

returns |>
  ggplot(aes(x = ret * 100)) +
  geom_histogram(bins = 100) +
  geom_vline(aes(xintercept = quantile_05),
    linetype = "dashed"
  ) +
  labs(
    x = NULL,
    y = NULL,
    title = "Distribution of daily Apple stock returns in percent"
  )
```

---
## Apple's stock returns: Historgram (II)

---
## Kenneth French's website

- Kenneth French provides data on his webpage including
  + Risk-free rates
  + Risk factors returns
  + Test assets for various tests
  
- Access via the `frenchdata` package

- Check out all available data on the webpage or via `get_french_data_list()`

---
## Kenneth French's data access

```r
library(frenchdata)
factors_ff_monthly_raw <- download_french_data("Fama/French 3 Factors")
factors_ff_monthly <- factors_ff_monthly_raw$subsets$data[[1]] |>
  transmute(
    month = floor_date(ymd(str_c(date, "01")), "month"),
    rf = as.numeric(RF) / 100,
    mkt_excess = as.numeric(`Mkt-RF`) / 100,
    smb = as.numeric(SMB) / 100,
    hml = as.numeric(HML) / 100)
```

---
## Risk-free rate

```r
factors_ff_monthly |> ggplot(aes(x = month, y = 100 * rf)) + 
  geom_line() +  labs(x = NULL, y = NULL, title = "Risk free rate (in percent)") 
```

---
## Macroeconomic data sources

- There are tons of data available from the FED and ECB

- Check out the packages `{fredr}` and `{ecb}` for easy access

- Alternatively, Ivo Welch provides some important predictors for asset pricing research on his website
  + Use the packages `{readxl}` and `{googledrive}` to retrieve it
  + Manipulating the data as suggested in Chapter *Accessing and Managing Financial Data* of #TidyFinance

---
## Implementing the CAPM

- The **CAPM** of Sharpe (1964), Lintner (1965), and Mossin (1966) originates the literature on asset pricing models

- Asset risk is the **covariance** of its return with the **market** portfolio return

- The higher the co-movement the less desirable the asset is, hence, the asset **price is lower** and the expected **return is higher**

- **Risk premium** is driven by investors' risk aversion and is equal to the expected value of excess market return

---
## Regression specification of stock `$i$`

`$$r_{i,t} - r_{f,t} = \alpha_i + \underbrace{\frac{Cov(r_i, r_m)}{\text{Var}(r_m)}}_{\beta_i} (r_{m,t} - r_{f,t}) + \varepsilon_{i, t}$$`

- Expected returns are determined by the **price of risk** (market risk premium) and the **co-movement** of asset `$i$` with the market, `$\beta_i$`

- To determine whether an asset  generates **abnormal returns** relative to the CAPM, we evaluate whether the intercept coefficient `$\alpha_i$` is statistically distinguishable from zero

---
## The market factor

- The market risk premium is the market excess return `$z_t = r_{m,t} - r_{f,t}$` 
- We proxy for the market with the value-weighted portfolio of all US based common stocks in CRSP (provided by Kenneth French)
- **Sharpe ratio** is computed as `$\frac{\hat{\mu_z}}{\hat{\sigma}_z}$`

```r
factors_ff_monthly |>  
    mutate(mkt_excess = 100 * mkt_excess) |>  
    summarise(across(mkt_excess, list(mean = ~ 12 * mean(.), 
                                      sd = ~sqrt(12) * sd(.), 
                                      Sharpe = ~sqrt(12) * mean(.)/sd(.)),
                     .names = "{.fn} (annualized)")) |> 
  kableExtra::kable()
```

| mean (annualized)| sd (annualized)| Sharpe (annualized)|
|-----------------:|---------------:|-------------------:|
|              8.14|            18.5|                0.44|

---
## CAPM - Introductory example (I)

- Implementation of the CAPM is a simple **linear regression** (estimated via OLS) with `lm`

- Let us look at an example for Apple Inc.
  + We compute monthly returns
  + Then, we run the CAPM linear regression

```r
apple_monthly <- returns |> 
  mutate(month = floor_date(date, "month")) |> 
  group_by(month) |> 
  summarize(ret = prod(1+ret) - 1,
            .groups = "drop") |> 
  left_join(factors_ff_monthly, by = "month") |> 
  mutate(ret_excess = ret - rf)
```

---
## CAPM - Introductory example (II)

- Implementation of the CAPM is a simple **linear regression** (estimated via OLS) with `lm`

- Let us look at an example for Apple Inc.
  + We compute monthly returns
  + **Then, we run the CAPM linear regression**

```r
lm(ret_excess ~ mkt_excess, data = apple_monthly) |> 
  broom::tidy() |> knitr::kable()
```

|term        | estimate| std.error| statistic| p.value|
|:-----------|--------:|---------:|---------:|-------:|
|(Intercept) |    0.018|     0.006|      2.98|   0.003|
|mkt_excess  |    1.374|     0.132|     10.42|   0.000|

---
## CAPM - Introductory example (III)

```r
apple_monthly |>  ggplot(aes(x = mkt_excess, y = ret_excess)) + geom_point() + 
  geom_smooth(method = "lm", se = FALSE) + 
  labs(x = "Market Excess Returns", y = "Apple Excess Returns")
```

---
## Bad news for CAPM?

- Figure shows decile portfolio sorts based on *lagged* beta (1 lowest, 10 highest)
- Each bar corresponds to the CAPM alpha of the value-weighted portfolio performance

---
background-image: url("images/wrds_logo.png")
background-position: 90% 60%
background-size: 400px

## Additional info: Where to get the best data?

- Gathering high quality data is the basis for any for research project

- Luckily, the Wharton Research Data Service (i.e., WRDS) exists

- WRDS combines many data providers in one, easy-to-use platform
  + CRSP,
  + Compustat,
  + TRACE,
  + Optionmetrics, and so much more..
  
- The Tidy Finance Chapter on **WRDS, CRSP, and Compustat** covers all details
  
---
## Additional info: Extensions to portfolio sorts

- The CAPM *test* is only one example of how to use portfolio sorts

- Portfolio sorts also extend to multiple characteristics at once with **multivariate portfolio sorts**

- The famous Fama and French (1992) model's factors come from a 2x3 sort on **size and book-to-market** (+ the market factor)

- The **factor zoo** shows how many applications portfolio sorts have in the academic literature

---
## Additional info: Researchs' discretion in portfolio sorts

- Researchers have to make **numerous decision** when conducting portfolio sorts:
  + How many portfolios?
  + How to weight portfolio returns?
  + Single or double sorts?
  + Sample construction rules?

- These decision are seemingly innocuous, but have a **large impact** on the estimates of risk premiums

- There is a clear potential for **p-hacking** and **data mining**

---
## Additional info: Methodological uncertainty in portfolio sorts

The degree of variation in risk premium estimates. See [Walter, Weber, and Weiss (2022)](https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4164117) for details.

---
class: chapter-slide

# Final remarks

---
## Conclusion

- Finance is great and academia is even better

- Check out [Tidy Finance](https://www.tidy-finance.org)

- You know some important concepts in **empirical asset pricing** 
  + You have learnt ways to implement them easily
  + You know where to look for more insights

---
class: middle, left
background-image: url("images/cover-book-r.jpg")
background-position: right
background-size: 350px

### Reach out with comments, questions, or <br> suggestions: <svg aria-hidden="true" role="img" viewBox="0 0 512 512" style="height:1em;width:1em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:blue;overflow:visible;position:relative;"><path d="M64 112c-8.8 0-16 7.2-16 16v22.1L220.5 291.7c20.7 17 50.4 17 71.1 0L464 150.1V128c0-8.8-7.2-16-16-16H64zM48 212.2V384c0 8.8 7.2 16 16 16H448c8.8 0 16-7.2 16-16V212.2L322 328.8c-38.4 31.5-93.7 31.5-132 0L48 212.2zM0 128C0 92.7 28.7 64 64 64H448c35.3 0 64 28.7 64 64V384c0 35.3-28.7 64-64 64H64c-35.3 0-64-28.7-64-64V128z"></path></svg> [contact@tidy-finance.org](mailto:contact@tidy-finance.org)

&nbsp;

## <svg aria-hidden="true" role="img" viewBox="0 0 512 512" style="height:1em;width:1em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:currentColor;overflow:visible;position:relative;"><path d="M464 256A208 208 0 1 1 48 256a208 208 0 1 1 416 0zM0 256a256 256 0 1 0 512 0A256 256 0 1 0 0 256zM294.6 135.1c-4.2-4.5-10.1-7.1-16.3-7.1C266 128 256 138 256 150.3V208H160c-17.7 0-32 14.3-32 32v32c0 17.7 14.3 32 32 32h96v57.7c0 12.3 10 22.3 22.3 22.3c6.2 0 12.1-2.6 16.3-7.1l99.9-107.1c3.5-3.8 5.5-8.7 5.5-13.8s-2-10.1-5.5-13.8L294.6 135.1z"></path></svg> visit [tidy-finance.org](https://www.tidy-finance.org)