Countercyclical Risk Premiums and Volatility

We will now relate the results from the previous sections to some theories in the literature, which investigate the countercyclicality of risk premiums and volatility, both directly and indirectly.

By doing so, we seek to provide motivation for modeling state-contingent preferences through volatility, which is substantiated in broader theoretical and empirical evidence than what we have provided.

The Leverage Effect and Volatility Feedback

The leverage effect is the effect of amplified volatility when the value of a firm falls. This relates to the fact that lower firm value increases the leverage of the firm, which leads to increased volatility of equity. This implies that stock volatility is dependent on stock prices. Despite the perhaps appealing economic intuition of this effect, empirical tests show that the leverage effect has little quantitative implications on market level (see for example Aydemir et al. (2005)), or at least cannot account for the full volatility response (see Schwert (1989)).

Another explanation could be the volatility feedback effect. The volatility feedback effect relies on the well-known and already mentioned persistence of volatility. More specifically, that news (positive or negative) increases both current and future volatility, as explained by Bekaert and Wu (2000) and Brunnermeier and Pedersen (2007). In addition, the volatility feedback effect is also based on a positive relationship between volatility and risk premiums. However, contrary to the leverage effect, causality runs from market volatility to the market risk premium, which is similar to the first example described through equation (4.3) in the previous section. More precisely, increases in volatility raise expected returns and lower current stock prices. In the case of good news, volatility has a dampening effect on the stock price increase resulting from the good news. In the case of bad news, volatility has an amplifying effect on the stock price decrease resulting from the bad news. Even though the empirical evidence is perhaps more supporting of the volatility feedback effect than the leverage effect, it should be mentioned that there is also conflicting empirical evidence for this theory, as pointed out by Bekaert and Wu (2000). Furthermore, the volatility feedback effect may be related to volatility spillover effects.

For example, Fornari and Mele (2013) provide explanations for volatility spillover effects, which include both passive volatility responses to economic conditions and direct volatility feedback from asset prices into the real economy. For the former, one of the examples that Fornari and Mele (2013) provide, is the increased value of waiting during uncertainty. More specifically, they address the fact that firms may freeze investments during uncertain times, as the value to wait increases in such periods. This could perhaps be amplified by a volatility feedback effect, as uncertainty could be prolonged with persistence of volatility. For the latter, Fornari and Mele (2013) explain how volatility might be related to procyclicality. This relates to the fact that

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if financial intermediaries are risk averse, or subject to institutional constraints, time-varying volatility in capital markets can affect lending and investment decisions. More specifically, they exemplify as follows:

"Consider the following arguments. In bad times, when financial volatility increases, the value of future collateral becomes more uncertain. In anticipation of this increased uncertainty, the volume of funds financial intermediaries would supply decreases, with a possible cost increase, thereby exacerbating the current economic conditions.".

This implies that the volatility feedback effect, and thereby the persistence of volatility, might be partly explained by quite measurable economic phenomenons. In fact, the example is closely related to liquidity spirals, which is what we will address in the next section.

Liquidity Spirals

Liquidity describes the degree to which an asset can be quickly sold without the price being affected, meaning that the seller has to sell at a discount to the asset’s fundamental value. A liquid market is a market where assets can be bought and sold quickly at their fundamental prices. Some define a market to be liquid if it can absorb liquidity trades from investors that have a sudden need for cash, without causing large shifts in the prices. Examples of less liquid markets are real estate and fine arts. The stock market is generally liquid in good and normal times, but as we will see, the stock market can become severely illiquid in bad times. This implies that the stock market has two equilibriums with regards to liquidity, one in good and normal states, and one in bad states. In this section, we present some of the findings in Brun-nermeier and Pedersen (2007) and Pedersen (2015), which provide economic explanations for the linkage between liquidity, volatility and market movements.

A liquidity crisis refers to a situation with acute shortage of liquidity. In general, a liquidity crisis occurs when there is an imbalance between the demand and supply of an asset. More specifically, when there is oversupply. This phenomenon tends to occur when the market enters a liquidity spiral. Before we discuss the details of a liquidity spiral, let us clarify two important terms, namely market liquidity risk and funding liquidity risk. From Pedersen (2015) we have

• Market liquidity risk: "Some securities have large transaction costs, and others can be traded at low cost. Securities with high transaction costs are said to be illiquid, in contrast to liquid securities, and securities with episodic spikes in transaction costs are said to have a lot of market liquidity risk."

• Funding liquidity risk: "Funding costs arise when a trader leverages his investments and must borrow money at a higher interest rate than the interest rate he earns on his cash holdings and short sale proceeds. Furthermore, leverage is associated with funding liquidity risk, that is, the risk that the trader cannot continue to finance his positions and is forced to liquidate in a fire sale."

Note that these two risks tend to be interrelated. In fact, Brunnermeier and Pedersen (2007), show how capital restrictions in funding, i.e. funding illiquidity, can induce market illiquidity.

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collateral and borrowed against. However, the entire value of the security cannot be borrowed against. The difference between the price of the asset and the loan has to be financed with equity, also known as the margin. Moreover, the traders must maintain a minimum amount of margin equity in their broker account at all times. This is known as the margin requirement.

When asset values decline, the posted margin gets closer to the margin requirement. Now, if at some point the margin equity becomes insufficient, the trader will receive a margin call from their broker, meaning that the trader will be forced to reduce positions or add cash. In addition, since repeated margin calls may lead to a termination of the broker account, traders will often try to keep excess margin capital. Hence, decreasing prices will at some point force traders to sell assets, as the margin is in risk of falling below the requirement.

A value at risk approach is usually applied by the financier to set the margin requirement, meaning that the trader has some accepted risk (or probability) of not being able to meet the requirement. Due to this VaR approach, it is likely that a persistent increase in volatility will contribute to a reduction in funding liquidity (i.e. funding constraints rise). Everything else held equal, traders will now be closer to the margin requirement, which means that there is a higher probability that asset sales will incur, i.e. that market liquidity is reduced. This is the essence of the liquidity spiral; the margin spiral (growing funding constraints) and theloss spiral (forced sales due to declines in asset prices) reinforce each other. The spiral starts when a shock causes leveraged investors to loose money, and some investors to reduce their positions due to funding problems. The selling pressure drives prices further down, which then again leads to additional losses for traders with related positions. In addition, the order imbalance and the fact that many traders usually provide liquidity, contributes to increased volatility in the market. Since increased volatility and illiquidity can cause an increase in funding constraints, traders might be forced to deleverage their positions. On top of this, capital redemptions from investors or management (for example in hedge funds), and risk-management considerations, increase the funding problems even more. Naturally, this will lead to another round of selling, which reinforces the effects above, and so on. This goes on until the fire sale stops, and the market starts to rebound again. This spiraling effect can be seen from figure 4.4.

In relation to our empirical investigation of volatility and returns, the theory of liquidity spirals can help explain why bad states are characterized by sharp declines in stock prices, compared to the more flatter increases in good and normal states. This follows from the fact that liquidity spirals get triggered when asset values are pushed down and investors become increasingly close to their capital constraints, essentially functioning as a multiplier effect for a declining market.

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82 • Chapter 5

times). The higher market volatility and illiquidity can lead prime brokers to increase margin requirements, forcing traders to deleverage their positions. In addition, risk management considerations push traders toward reducing posi-tions, and redemptions of capital from investors (or management) add to the funding problems. For all these four reasons, funding problems continue to grow, leading to a second round of selling, and so on, until the fire sale ends and markets can start to rebound.

A stylized price path during a fire sale is shown in figure 5.6. Prices drop sharply as traders sell, reach the bottom when the deleveraging is over, rebound as they gravitate toward fundamentals when some traders releverage and other investors arrive, and stabilize at the new equilibrium price, which is temporar-ily lower than before due to the exit of traders, capital, and funding.

A liquidity spiral implies that there exists a crash risk that is difficult to detect during normal trading days. Said differently, return distributions are in-herently non- normal: While price changes are driven by fundamental news on most days, price changes are driven by forced selling during liquidity spirals.

Liquidity spirals also change correlations across securities since, during a li-quidity event, the prices of securities held by traders with funding problems start to co- move, even if their fundamentals are unrelated. Indeed, a liquidity crisis is contagious since losses in one market can lead to fire sales in other markets, hurting more traders and spreading the crisis. When a liquidity spiral

Funding problems

Reduced positions

Higher margins

Prices move away from fundamentals

Losses on positions Tighter risk management

Redemption of capital Initial shock

Figure 5.5. Liquidity spiral.

Figure 4.4: Liquidity spirals. Source: Pedersen (2015)

To conclude our discussion on liquidity, we will present a brief summary of the findings in Brunnermeier and Pedersen (2007).

Their model implies that market liquidity..

(a) can suddenly dry up

(b) has commonality across securities

(c) is related to volatility

(d) is subject to ’flight to liquidity’

(e) comoves with the market

They predict that..

1. a shock to speculators’ capital is a state variable affecting market liquidity and risk premia

2. a reduction in capital reduces market liquidity, especially if capital is already low (a non-linear effect) and for high-margin securities

3. margins increase in illiquidity if the fundamental value is difficult to deter-mine

4. speculators’ returns are negatively skewed (even if they trade securities without skewness in the fundamentals) Considering our previous discussions of the countercyclicality of volatility and risk premiums, some of the most interesting findings are perhaps predictions 1 and 2. Firstly, prediction 1 is interesting because it implies that exogenous volatility shocks affect the risk premium of investors, as seen from equation (4.3). Moreover, a condition for this to be true is that

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premiums to increase if volatility was expected to rebound instantaneously to a normal level after an increase. However, if volatility is persistent, then it is natural that risk premiums increase. This can be related to our previous results of negative co-movement between ex-ante returns and ex-post volatility. Moreover, from prediction 2 we have that a reduction in capital has a small effect when traders are far away from their capital constraints, but a large effect when investors are close to their constraints. This gives strong economic justification to why volatility increases non-proportionally in bad states of the economy. Lastly, point (d), which means that investors prefer liquid assets in illiquid times, relates strongly to the ’flight to quality’ phenomenon discussed in section 3.2, and thus provides another dimension to the topic.

Time-Varying Risk Aversion

As was pointed out in section 4.2.1, volatility could also be endogenous, i.e. causality runs from the risk aversion of investors to volatility, not the other way around. Mele (2007) addresses this, but points out that for countercyclical risk premiums to lead to countercyclical volatility, risk premiums must increase more in bad times than in good times. More specifically, Mele (2007) develops a theoretical framework in which the discount rate of investors depends on the economic state, i.e. the real economy, and where the discount rate becomes exponentially larger the worse the economic state becomes. This means that risk aversion rises more in bad times than in good times, which induces greater fluctuation in asset prices in bad times compared to good times. We will not go further into the theoretical framework of Mele (2007), as it is quite complicated, but we note that there is empirical support for the framework.