class: center, middle, inverse, title-slide .title[ # Lecture 15 ] .subtitle[ ## Climate Risk and Financial Instruments ] .author[ ### Ivan Rudik ] .date[ ### AEM 4510 ] --- exclude: true ```r if (!require("pacman")) install.packages("pacman") pacman::p_load( tidyverse, xaringanExtra, rlang, patchwork ) options(htmltools.dir.version = FALSE) knitr::opts_hooks$set(fig.callout = function(options) { if (options$fig.callout) { options$echo <- FALSE } knitr::opts_chunk$set(echo = TRUE, fig.align="center") options }) ``` ``` ## Warning: 'xaringanExtra::style_panelset' is deprecated. ## Use 'style_panelset_tabs' instead. ## See help("Deprecated") ``` ``` ## Warning in style_panelset_tabs(...): The arguments to `syle_panelset()` changed in xaringanExtra 0.1.0. Please ## refer to the documentation to update your slides. ``` --- # Roadmap 1. .hi[Weather markets (Schlenker and Taylor, 2021):] do traders forecast weather and climate? 2. .hi[Municipal bond markets (Painter, 2020):] is sea level rise capitalized into municipal financing costs? - Marginal damages 3. .hi[Prediction markets (Meng, 2017):] what is the probability of environmental regulation? 4. .hi[Equity markets (Meng, 2017):] what is the financial impact of expected environmental regulation? - Marginal abatement costs --- class: inverse, center, middle name: overview # Weather markets <html><div style='float:left'></div><hr color='#EB811B' size=1px width=796px></html> --- # Betting on the weather The purpose of this lecture is to see whether financial markets price climate risk -- Our first step: prove to ourselves that traders even recognize climate change -- How? -- Studying the market for weather derivatives --- # Betting on the weather <div style= "float:right;position: relative;"> <img src="files/15-cme-cities.png" width="700px" /> </div> Weather derivatives are a way for weather-exposed firms to manage climate risk - Which kind of firms? -- CME offers contracts based on weather indices in 13 cities (mostly US) --- # Betting on the weather Winter contracts are based on .hi[heating degree days (HDD)] - HDD = max(0, `\(65^\circ\)`F - daily average temperature): how much colder than 65 -- Summer contracts are based on .hi[cooling degree days (CDD)] - CDD = max(0, daily average temperature - `\(65^\circ\)`F): how much warmer than 65 -- Idea is `\(65^\circ\)`F is about where you would heat or cool a building to during the day --- # Betting on the weather How do the contracts work? -- The contracts are bought and sold like regular assets, but the settlement price is explicitly based on the realized HDD/CDD -- CME contracts work where the settlement price is: 20 `\(\times\)` CDD/HDD -- Example: - If the July CDD contract is trading at 300 CDDs, the contract costs `\(20 \times 300 = 6000\)` - If actual July CDDs are 330, a buy-side trader profits: `\(20 \times (330 - 300) = 600\)` --- # Betting on the weather Who might buy/sell weather contracts? -- Natural gas suppliers in the Northeast -- - Natural gas suppliers profit more when winter is cold (why?) -- Do these firms want to buy or sell winter HDD contracts to manage risk? -- .hi[Sell] -- , Why? --- # Betting on the weather Selling a winter HDD contract is a bet that HDDs will be low `\(\rightarrow\)` winter will be warm -- This bet pays off when natural gas revenues are low and helps manage risk -- Example: - The winter HDD contract is trading at 1250 - At 1250 HDDs, NYSEG expects to generate $80 million in profit - An increase in HDDs of 1 increases profits by $80,000 --- # Betting on the weather Example: - The winter HDD contract is trading at 1250 - At 1250 HDDs, NYSEG expects to generate $80 million in profit - An increase in HDDs of 1 increases profits by $80,000 -- If NYSEG sells `\(Y\)` winter HDD contracts, and the realized winter HDD is `\(HDD_{actual}\)`: - Its futures market profits are: `\(Y \times 20 \times (1250 - HDD_{actual})\)` - Its natural gas profits are: `\(80,000,000 + 80,000 \times (HDD_{actual} - 1250)\)` Futures profits down in `\(HDD_{actual}\)`, natural gas profits go up --- # Betting on the weather Example: - The winter HDD contract is trading at 1250 - At 1250 HDDs, NYSEG expects to generate $80 million in profit - An increase in HDDs of 1 increases profits by $80,000 How many contracts should NYSEG sell if it wants to eliminate all risk? -- Eliminate risk by setting sum of futures market profit and HDD-related natural gas profit to zero -- `$$Y \times 20 \times (1250 - HDD_{actual}) + 80,000 \times (HDD_{actual} - 1250) = 0$$` `$$Y = 4,000 \,\, \text{contracts}$$` --- # Betting on the weather Who else might participate in these markets (summer or winter)? - Farmers - Amusement parks - Electricity utilities - Snow plow services - People who think they have better private information -- The market price should aggregate everyone's beliefs about weather -- If traders actually internalize climate information, we should see weather derivative prices respond to weather and climate forecasts --- # Betting on the weather Schlenker and Taylor (2021) study whether the contract prices capitalize expected short-run weather, and long-run climate change -- The first step is to see whether short-run weather is capitalized into the price -- How do they do it? -- 1. Compute the .hi[weather anomaly:] how much warmer or cooler a day is relative to its average (accounting for overall warming over time) 2. Compute whether the change in the price from open to close on a given day is associated with weather anomalies --- # Betting on the weather <div style= "float:right;position: relative;"> <img src="files/15-forecast-skill.webp" width="600px" /> </div> 1-3 day forecasts are essentially perfect now 10 day forecasts have 40% "skill": 40% smaller error than if you just assumed temperature would be its long-run average --- # Betting on the weather <div style= "float:right;position: relative;"> <img src="files/15-forecast-skill.webp" width="600px" /> </div> Forecasts >10 days out have little skill `\(\rightarrow\)` little information value Forecasts 1-3 days out have near-perfect skill, their information is probably already capitalized by prior forecasts 5-7 days ago --- # Betting on the weather <div style= "float:right;position: relative;"> <img src="files/15-forecast-skill.webp" width="600px" /> </div> We should expect forecasts 3-10 days out to matter the most for contract prices We should expect little to zero effect of 1-3 day forecasts, and 10+ day forecasts --- # July CDD prices for Laguardia airport <div style= "float:right;position: relative;"> <img src="files/15-weather-futures-prices.png" width="600px" /> </div> July in NY averages about 400 CDDs Each year from 2001-2020 (different color lines) differs in terms of actual CDDs (price at 0), and expected CDDs (prices to the left of 0) --- # July CDD prices for Laguardia airport <div style= "float:right;position: relative;"> <img src="files/15-weather-futures-prices.png" width="600px" /> </div> In general, prices don't move much further than 10 days before the start of July `\(\rightarrow\)` consistent with short-run 10+ day forecasts not being skillful Differences across years can be from long-run trends, El Nino, etc --- # July CDD prices for Laguardia airport <div style= "float:right;position: relative;"> <img src="files/15-weather-futures-prices.png" width="600px" /> </div> Once we near the actual month (about -40), forecasts are skillful They start trending toward their realized values (at 0) From -30 to 0 we are .hi[in] the actual month and observe some of the realized CDDs --- # Betting on the weather So far we just eyeballed data, but now we want to actually compute whether the change in the price from open to close on a given day is associated with weather anomalies -- Schlenker and Taylor estimate a regression model of how weather anomalies up to 1 week before some day `\(t\)`, and up to 3 weeks after day `\(t\)` affect the change in the contract price during day `\(t\)` -- Let's think through the intuition before seeing the results --- # Betting on the weather Schlenker and Taylor estimate a regression model of how weather anomalies up to 1 week before some day `\(t\)`, and up to 3 weeks after day `\(t\)` affect the change in the contract price during day `\(t\)` -- Should weather anomalies 3 days ago (i.e. in the past) affect the change in the contract price today? -- .hi[No!] It should have already been priced in --- # Betting on the weather Schlenker and Taylor estimate a regression model of how weather anomalies up to 1 week before some day `\(t\)`, and up to 3 weeks after day `\(t\)` affect the change in the contract price during day `\(t\)` -- Should weather anomalies in the future affect the change in the contract price today? -- .hi[Yes!] Skillful forecasts should predict future weather anomalies, if traders use these forecasts then future weather anomalies should affect the current price change - Suggests forecasts 10+ days ahead might not affect the price --- # Futures prices predict future weather <div style= "float:right;position: relative;"> <img src="files/15-futures-event-study.png" width="600px" /> </div> X-axis: days before (left) and after (right) current trading day Y-axis: change in contract price given a `\(1^\circ\)`C higher CDD anomaly -- Black line: today's change in the CDD contract price changes when CDDs are higher by 1 degree at `\(\tau\)` days in the future Negative `\(\tau\)`s are past days / weather anomalies, positive `\(\tau\)`s are future days / weather anomalies --- # Futures prices predict future weather <div style= "float:right;position: relative;"> <img src="files/15-futures-event-study.png" width="600px" /> </div> Does past weather affect changes in current prices? -- .hi[No!] Capitalization is close to 0 for all `\(\tau < 0\)` -- Does future weather affect changes in current prices? -- .hi[Yes!] Up to about 2 weeks into the future --- # Futures prices predict future weather <div style= "float:right;position: relative;"> <img src="files/15-futures-event-study.png" width="600px" /> </div> What does all this mean? -- Since future weather can only affect today's contract price through forecasts (future weather hasn't happened yet!)... -- This means that .hi[traders respond to weather forecasts] -- Traders also are using the info correctly because prices are .hi[positively] associated with weather anomalies --- # Futures prices predict future weather <div style= "float:right;position: relative;"> <img src="files/15-futures-event-study.png" width="600px" /> </div> Does the weather anomaly get fully capitalized? - Is the market accurately pricing in future weather? -- If so the .hi[total capitalization] of a 1 CDD anomaly should add up to 1 -- The sum (integral) of the values of the black line over all `\(\tau\)` equals 1 if the market is pricing correctly --- # Futures prices predict future weather <div style= "float:right;position: relative;"> <img src="files/15-futures-cumulative.png" width="600px" /> </div> Black line: the .hi[cumulative] sum of the previous black line -- Adding up over all days gives a sum of .hi[1] -- The market fully internalizes short-run weather! -- It's fully internalized using forecasts up to 14 days ahead --- # Futures prices and long-run climate Weather futures capitalize short-run weather -- What about long-run changes in climate? -- If so, the long run trends in futures prices should match either: 1. Long run trends in weather 2. Predicted trends from climate models --- # Futures prices predict long-run climate <div style= "float:right;position: relative;"> <img src="files/15-long-run-futures.png" width="700px" /> </div> Y-axis: CDD/HDD relative to the city average (0 is average) Lines: contract price (dark green), actual weather CDDs/HDDs (red), climate model predicted CDD/HDDs (blue/neon) -- What stands out? --- # Futures prices predict long-run climate <div style= "float:top;position: relative;"> <img src="files/15-long-run-futures.png" width="10000px" /> </div> Longer-run changes in futures prices closely track .hi[climate models], weather to a lesser extent --- class: inverse, center, middle name: overview # Municipal bond markets <html><div style='float:left'></div><hr color='#EB811B' size=1px width=796px></html> --- # Bonds .hi[Bonds:] what are they? -- > [Wiki] A bond is a type of security under which the issuer (debtor) owes the holder (creditor) a debt, and is obliged – depending on the terms – to repay the principal (i.e. amount borrowed) of the bond at the maturity date as well as interest (called the coupon) over a specified amount of time. -- Bonds are assets, can be traded on secondary markets --- # Bonds Why do bonds exist? -- Bonds are a way to raise money: - At time `\(t\)`, issue bonds with maturity `\(T\)` - Get money from creditors - Pay back interest/coupon over time between `\(t\)` and `\(T\)` - Pay back principal at some future date `\(t+T\)` -- We will focus on .hi[municipal bonds (munis)] for pricing climate risk, why? --- # Municipal bonds Why munis for pricing climate risk? -- Suppose Starbucks has coffee packaging plants in Miami -- Miami is expecting disastrous sea level rise, what can Starbucks do to manage it? -- Move its plants somewhere else away from the ocean -- The city of Miami does not have the same option: it bears the full potential cost of sea level rise --- # Municipal bonds How do munis work? -- Local governments issue munis for financing public projects (roads, infrastructure, etc) -- Debt is typically paid back in a pre-specified way - .hi[General obligation bonds:] paid using tax revenue - .hi[Revenue bonds:] project-specific revenue (e.g. parking garage revenues) -- General obligation bonds are typically less risky --- # Municipal bonds How do bonds work? -- They have some .hi[face value] `\(FV\)`, the price paid when the bond matures -- They pay out a .hi[coupon] (assume annually) `\(C\)` -- They trade on the bond market at some .hi[price] `\(P\)` which will depend on: - The face value - The coupon - When the bond matures - *Other underlying economic conditions* --- # Municipal bonds We can define the .hi[yield to maturity] `\(y\)` as: `$$P = \left[\sum_{t=1}^T \frac{C}{(1+y)^t}\right] + \frac{FV}{(1+y)^T}$$` `\(y\)` is the effective interest rate the investor is getting on a price `\(P\)` bond -- Given some price `\(P\)`, a higher yield `\(y\)` means that the flow of coupons `\(C\)` or face value `\(FV\)` must be higher -- Given some coupon `\(C\)` and face value `\(FV\)`, a higher yield `\(y\)` means a lower price `\(P\)` --- # Municipal bonds Why would future climate risk be capitalized into munis? Examples for why? -- 1. If climate change (e.g. sea level rise) destroys infrastructure, raises municipal costs, raises risk of bankruptcy and non-payment of the bond -- 2. If climate change induces people to leave, this shrinks the tax base, makes it more difficult for the municipality to pay back the bond, raises risk of non-payment -- Factors like these should be priced into the bond if traders understand climate risk --- # Municipal bonds Let's work with a simple one-period zero coupon example: `\(C=0\)`, `\(T=1\)`, `\(FV = 105\)`: `$$P = \frac{105}{(1+y)^1}$$` Suppose there is no climate change and the market yield is 5%, the price of the muni is: -- `$$P = \frac{105}{1+.05} = 100$$` --- # Municipal bonds Now suppose we are considering the same muni, but there is a 7% chance that the city will be destroyed by sea level rise before next year - Additional 7% chance that the bond will not be paid To bear this additional risk, traders will demand a higher yield (lower price) --- # Municipal bonds We can solve for the new price: `$$P = \frac{105}{1+.05} \times \underbrace{(1 - .07)}_{1/(1+.075)} = \frac{105}{1+.05} \times \frac{1}{1+.075}=93$$` and the associated yield: `\begin{align} \frac{1}{1+y} &= \frac{1}{1+.05} \times (1 - .07) = \frac{.93}{1.05} \\ \Rightarrow y &= \frac{1.05}{.93} - 1 = .129 \end{align}` --- # Municipal bonds The additional 7% climate risk: - Decreased the price by 7% from 100 to 93 - Increased the yield by 7.9 percentage points from 5% to 12.9% -- As climate risk rises, traders demand greater yields to offset the chances of non-payment -- We can measure the financial risks of climate change by looking at how places with different climate risk have munis with different yields --- # Municipal bonds and sea level rise Painter (2020) looks at how sea level rise (SLR) risk affects bond yields - Also looks at other things outside what we're doing in class -- How should SLR affect bond yields of different maturities? -- SLR is a slow phenomenon, will matter increasingly over the next century -- - non-existent in the short run: short-term bonds shouldn't be affected -- - only shows up in the long run: long-run bonds should be affected if investors care --- # Municipal bonds and sea level rise .center[ <img src="files/15-climate-risk-table.png" width="800px" /> ] Climate risk: expected percent loss of city GDP Where is the climate risk? --- # Municipal bonds and sea level rise .center[ <img src="files/15-raw-bond-data.png" width="800px" /> ] What does the raw data say about climate/SLR exposed and non-exposed munis? -- Climate(-exposed) bonds are 8 basis points more expensive to offer 11 basis points higher yield --- # Yield <div style= "float:right;position: relative;"> <img src="files/15-yield-results.png" width="700px" /> </div> Comparing munis offered in the same state and year, controlling for other factors: .hi[Areas at risk for SLR must offer greater yields by 16pp] --- # Gross spread <div style= "float:right;position: relative;"> <img src="files/15-gross-spread-results.png" width="700px" /> </div> They have higher gross spreads (higher underwriter search costs): 10-15bp higher for long-term bonds --- # Maturities <div style= "float:right;position: relative;"> <img src="files/15-maturity-results.png" width="700px" /> </div> Effect is larger for longer-maturity bonds: bonds maturing --- # Credit ratings <div style= "float:right;position: relative;"> <img src="files/15-credit-rating.png" width="700px" /> </div> SLR matters most for bonds with lower ratings: Non-high grade munis costs are 50bp higher with higher climate risk --- # What does this all mean? We've seen that places more exposed to SLR: - Must offer higher yields on long-term bonds, with yields increasing in time to maturing - Incur higher gross spreads - Must offer even higher yields if they do not have a high credit rating -- Think about the long-run equilibrium of economic activity, where people live, etc -- What does this suggest will happen? --- # What does this all mean? 1. Capital is becoming more expensive in SLR-exposed cities -- 2. These cities will be less able to fund public projects (e.g. parks), making them less desirable -- 3. Marginal households who value these projects move elsewhere -- 4. Tax base shrinks `\(\rightarrow\)` feedback loop -- Does this tell the whole story? --- # What does this all mean? Alternatively: 1. Capital is becoming more expensive in SLR-exposed cities -- 2. These cities will be less able to fund public projects (e.g. parks), making them less desirable -- 3. City funds adaptation projects (e.g. sea walls) to reduce exposure, decreasing yields and capital costs -- In both cases, muni markets serve an important function for directing resources and people to the most productive areas --- # Prediction markets <div style= "float:right;position: relative;"> <img src="files/15-predict-it.png" width="700px" /> </div> Prediction markets are where traders bet on binary outcomes -- Will Republicans win the senate? -- How does it work? --- # Prediction markets <div style= "float:right;position: relative;"> <img src="files/15-predict-it.png" width="700px" /> </div> You can buy a share (asset) for whether the event will happen or not happen -- The price of this share is: - 72c for Republicans winning - 32c for Democrats winning --- # Prediction markets After the election: - The shares for the winning side pay off $1 each - The shares for the losing side are worth $0 What does the prediction market tell us? -- Let's think about the economics of the market -- Let: - The cost of a share be `\(c\)` dollars - Your belief about the probability of an event happening be `\(p\)` percent --- # Prediction markets Based on your beliefs about the event, your expected profit from buying a share is: `\([p \times 1 + (1-p) \times 0] - c\)` -- You make a profit if `\(p > c\)`, you make a loss if `\(p < c\)` -- Suppose `\(p > c\)`, what happens? -- You expect a profit, you start buying shares... -- This drives up the price `\(c\)` -- This is true as long as `\(p > c\)` --- # Prediction markets Suppose `\(p < c\)`, what happens? -- You expect a loss, you start selling your existing shares... -- This drives down the price `\(c\)` -- This is true as long as `\(p < c\)` -- Individual profit motives always drive `\(c\)` toward `\(p\)` -- .hi[The price of the share tells us the market's expectation about the probability of the event!] --- # Waxman-Markey The most important US climate policy of the 2000s was the 2009 American Clean Energy and Security Act: aka .hi[Waxman-Markey (WM)] -- What did WM propose to do? -- Set an annual cap on `\(CO_2\)` emissions that starts in 2012 and declines over time to: - 83% of 2005 levels in 2020 - 58% of 2005 levels in 2030 - 17% of 2005 levels in 2050 --- # Waxman-Markey WM allowed permits to be .hi[traded] -- and also .hi[banked and borrowed] - .hi[Banked:] permits not used this year can be saved - .hi[Borrowed:] can emit more than retired permits today on the promise of retiring the extra necessary permits in the future - Borrowing had an 8% interest rate --- # Waxman-Markey How did WM allocate permits ([info here](https://grist.org/article/2009-05-15-waxman-markey-permit-proposal/))? Most were freely allocated: - .hi[35%] of permits go to electric utilities -- - .hi[9%] of permits go to natural gas distributors -- - .hi[1.5%] of allowances go to states to buffer users of home heating oil and propane -- - .hi[15%] go to .hi-blue[energy-intensive, trade-exposed] industries - Over 5% energy intensity & 15% trade intensity `\(\rightarrow\)` free permits -- Rest are auctioned or given to different government agencies --- # Waxman-Markey: the history June 26, 2009: Waxman-Markey passes the House of Representatives (219-212) - 211/255 Democrats vote yes, 8/176 Republicans vote yes - First cap and trade bill to be passed by congress! - Still needs to pass the senate -- 2009/2010 senate: 59 Democrats/independents, 41 Republicans -- All Democrats and one Republican need to vote yes for it to pass the senate -- It took until April 2010 to convince one Republican ... who was it? --- # Waxman-Markey: the history <div style= "float:right;position: relative;"> <img src="files/15-lindsey-graham.jpeg" width="300px" /> </div> -- Lindsey Graham! -- On Thursday April 22, 2010, after months of negotiation: -- John Kerry, Joe Lieberman, and Lindsey Graham complete the senate-version of the bill -- The unveiling of the bill was scheduled for Monday April 26, 2010 -- You won't believe what happens next --- # Waxman-Markey: the history <div style= "float:right;position: relative;"> <img src="files/15-harry-reid.jpg" width="300px" /> </div> -- Senate Majority Leader Harry Reid (Nevada) was up for re-election in 2010 -- In April, he was trailing his Republican challenger -- On Thursday April 22, 2010 Senator Reid announces the Senate will start working on an immigration bill -- This makes political sense: at the time Nevada was 30% Hispanic/Latino -- The Senate calendar couldn't accommodate both climate and immigration legislation: Lindsey Graham thought it was cheap point scoring from Reid --- # Waxman-Markey: the history <div style= "float:right;position: relative;"> <img src="files/15-arizona.svg" width="300px" /> </div> -- On April 13/19, 2010 the Arizona state house and senate voted to pass .hi[SB 1070:] the Support our Law Enforcement and Safe Neighborhoods Act -- aka the .hi[Show Me Your Papers Act] -- SB 1070 required state law enforcement to ask suspicious people to present proof of legal immigration status -- , it also made it a crime to not have immigration papers on hand -- SB 1070 was .hi[incredibly] controversial -- It was unclear whether governor Jan Brewer would sign it --- # Waxman-Markey: the history <div style= "float:right;position: relative;"> <img src="files/15-jan-brewer.jpg" width="300px" /> </div> -- Friday April 23, 2010 Jan Brewer signs SB 1070 into law -- This was seen by some as legalized racial profiling of the Latino population -- Immigration becomes the focal point of congress -- 10PM Friday April 23, 2010: Graham's aide e-mails Lieberman's aide "Sorry buddy." -- Graham formally states he refuses to delay a climate bill for immigration and abandons his legislation --- # Waxman-Markey: the probabilities <div style= "float:right;position: relative;"> <img src="files/15-intrade-prices.png" width="600px" /> </div> .hi[Jun 26:] House passes WM .hi[Nov 4:] Graham joins senate effort .hi[Dec 20:] Copenhagen negotiations .hi[Jan 19:] Scott Brown wins Mass. senate seat .hi[Apr 23:] Graham drops support .hi[July 22:] Senate drops cap and trade --- # Waxman-Markey: the probabilities <div style= "float:right;position: relative;"> <img src="files/15-intrade-prices.png" width="600px" /> </div> Markets almost never thought WM was a favorite to pass! Even around Graham-Kerry-Lieberman announcement, probabilities were only 20% --- # Waxman-Markey: the probabilities <div style= "float:right;position: relative;"> <img src="files/15-intrade-prices.png" width="600px" /> </div> The prediction market prices tell us the market's expectation of climate legislation being implemented The legislation itself tells us how much emissions must be reduced With one more piece of information - the .hi[costs] of the legislation - we can back out the `\(CO_2\)` MAC --- # Equity markets We can back out the costs of the legislation from .hi[stock return] data -- Let's write down a simple model of stock returns and firm value to see how -- - `\(P_t:\)` probability of WM passing - `\(V^{WM}_{i,t}:\)` the value of firm `\(i\)` on day `\(t\)` if WM .hi[passes] - `\(V^{-}_{i,t}:\)` the value of firm `\(i\)` on day `\(t\)` if WM .hi[does not pass] - `\(V_{i,t}:\)` the expected value of firm `\(i\)` on day `\(t\)` based on the probability of WM passing: - `\(V_{i,t} = P_t \times V^{WM}_{i,t} + (1 - P_t) \times V^{-}_{i,t}\)` - `\(V_{i,t}\)` is the prediction market weighted average To keep it simple, assume nothing else is changing besides WM probabilities --- # Equity markets `$$V_{i,t} = P_t \times V^{WM}_{i,t} + (1 - P_t) \times V^{-}_{i,t}$$` -- Define `\(E^{WM}_i\)` as the percentage effect of WM on firm value: `\(E^{WM}_i = \frac{V^{WM}_{i,t} - V^{-}_{i,t}}{V^{-}_{i,t}}\)` `\(E^{WM}_i\)` tells us how much firm value changed as a result of WM going into effect -- Rewrite `\(V_{i}\)` in terms of `\(E^{WM}_i\)`: `$$V_{i,t} = V^{-}_{i,t} \times (1 + P_t \, E^{WM}_i)$$` The firm value on day `\(t\)` is the value of the firm if WM doesn't pass `\((V^{-}_{i,t})\)`, but scaled up by the effect of WM `\((E^{WM}_i)\)` times the chances WM passes `\((P_t)\)` --- # Equity markets `$$V_{i,t} = V^{-}_{i,t} \times (1 + P_t \, E^{WM}_i)$$` .hi[Stock returns] `\(r_{i,t}\)` are the change in log firm value: `$$r_{i,t} = \ln V_{i,t} - \ln V_{i,t-1} = \ln \frac{V_{i,t}}{V_{i,t-1}}$$` We can write this as: `$$r_{i,t} = \ln \frac{V^{-}_{i,t} \times (1 + P_t \, E^{WM}_i)}{V^{-}_{i,t-1} \times (1 + P_{t-1} \, E^{WM}_i)}$$` --- # Equity markets `\begin{align} r_{i,t} &= \ln \frac{V^{-}_{i,t} \times (1 + P_t \, E^{WM}_i)}{V^{-}_{i,t-1} \times (1 + P_{t-1} \, E^{WM}_i)} \\ r_{i,t} &= \ln \frac{V^{-}_{i,t}}{V^{-}_{i,t-1}} \ln \frac{(1 + P_t \, E^{WM}_i)}{(1 + P_{t-1} \, E^{WM}_i)} \\ r_{i,t} &= \ln \frac{V^{-}_{i,t}}{V^{-}_{i,t-1}} \times \left[ \overbrace{\underbrace{\ln (1 + P_t \, E^{WM}_i)}_{\approx P_t \, E^{WM}_i}}^{\ln (1+x) \approx x} - \overbrace{\underbrace{\ln (1 + P_{t-1} \, E^{WM}_i)}_{\approx P_{t-1} \, E^{WM}_i}}^{\ln (1+x) \approx x} \right] \\ r_{i,t} &= P_{t} E^{WM}_i - P_{t-1} E^{WM}_i + \underbrace{\ln \frac{V^{-}_{i,t}}{V^{-}_{i,t-1}}}_{\substack{\ln 1 = 0 \\ \text{if not changing}}} \end{align}` --- # Equity markets `$$r_{i,t} = P_{t} E^{WM}_i - P_{t-1} E^{WM}_i = (P_t - P_{t-1}) \times E^{WM}_i$$` If no other determinants of firm value are changing from day-to-day, the stock return tells us the effect of WM on firm value scaled by the change in the probability that WM happens -- We have data on stock returns `\(r_{i,t}\)`, we have data on market expectations `\(P_t, P_{t-1}\)`, we can then get `\(E^{WM}_i\)` --- # Equity markets: getting MAC <div style= "float:right;position: relative;"> <img src="files/15-wm-rdd-plot.png" width="600px" /> </div> .hi[X-axis:] energy intensity .hi[Red line:] cut off for free permits .hi[Y-axis:] change in firm value from WM -- WM generally has a bigger negative effect on firm valuations the more energy intensive the firm -- .hi[But:] getting free permits mitigates the negative impact! --- # Equity markets: getting MAC <div style= "float:right;position: relative;"> <img src="files/15-wm-rdd-plot.png" width="600px" /> </div> At an energy intensity of 5%, WM reduces firm value by about 6%! This is the present value of the expected costs of having to buy permits in an auction versus getting them for free How do we get the MAC (i.e. the implied permit price)? --- # Equity markets: getting MAC - `\(\tau\)`: permit price / MAC - `\(E_t\)`: emissions - `\(r\)`: interest rate The present value of the expected costs is: `\(.06 = \sum_{t=0}^\infty \frac{\tau \times E_t}{(1+r)^t}\)` -- If we have forecasts about emissions and the interest rate, we can solve for `\(\tau\)`! --- # Equity markets: getting MAC <div style= "float:right;position: relative;"> <img src="files/15-mac-table.png" width="600px" /> </div> Using the listed decline in emissions and a 5% interest rate gives us these MACs -- In 2010 MACs were...quite low! At most `\(18/tCO_2\)`, about 1/10 the current best estimate of MD, 1/3 the best estimate in 2010 -- What does this imply about WM? -- If MAC < MD, then the cap is .hi[below] the socially efficient level