Category: Finance

The Interview about the Principles for Changing World Order

by Ray Dalio

Five Factors:

  1. Economy, Debt, Money, Market
  2. Internal Order or Disorder/Conflict
  3. External Order or Disorder (Power Rivalries)
  4. Acts of Nature (Impact of Climates)
  5. Technologies (the advance of productivity)

Cycles Factors, as the below three, generate the cycle. (, are marked by wars. Starting the cycle at the end of WW II.)

  1. Internal Order – Productivity increase
  2. Debt raises relative to Incomes. (Debt is money, and debt means more buying power.) Increase the gaps of wealth, -> Internal Conflicts start to emerge
  3. External Conflict:

Climates, and Technologies (Mans inventiveness, new technologies)

Apply those five factors into the current world.

  • The current Debt Climate condition:

    Currently,

    Private debt sectors (individuals) get more and more indebted.

    Public debt sector take on the debt, and the central bank is supporting that effort.

    On a cyclical basis, total debt relative to GDP continuing to rise near its high.

    Debt service cost (a function of interest rate) increase, and public sector takes the burden.

    Then, Public sector starts to get indebtedness.

    That is the short-term cycle.

The cycle for development, Ray considers there are four stages.

  1. A poor country that has no capital accumulation starts to recognise the poverty.

    Country gets money to get capital formation, and conduct infrastructure (such as build roads). Do not waste that money, and put money into productive uses.

  2. Mentality. As the country getting richer, it still think it is not rich enough, is still poor.

  3. The country keeps getting richer, and start to realise it do not have to work that hard, and start to enjoy the life.

  4. As there are less works, the country gets poor, but still think itself is rich. So start to borrow money.

How to create a portfolio.

  • has a diversified portfolio that is able to absorb risks and unforeseen.

  • The types of assets in the portfolio might include

    1. Inflation index bonds
    2. Gold
    3. Real Rates
    • Avoid the credit risk. (The above three are the government obligations, so less credit risks are there)
    • Such as, we short Inflation index bond and long Gold (we could avoid the credit risks, and diversify the portfolio with certain target)

CFA Learning Notes and Materials

11th April 2024

I have passed the CFA III level exam, and been granted the chart.

For any errates and insights, please free to contact to me.

Here below are my learning footprints for CFA level III. All files are converted to .html as you will find in the following . If you need the raw markdown codes, please move to my Github Repo.

P.S. there are typos and miswritten parts in the notes. Welcome to find me and help me update those mistakes. Or, probably I will update them if I fail the level III exam (in that I would review those notes). 🙂

Best Wishes
FZ

  1. CME
    P.S. BehaviouralFinance
  2. AssetAllocation
  3. Derivatives&Exchange
  4. Fixed-Income
  5. Equity
    P.S. Equity-Active
  6. Fixed-Income
  7. Alternatives
  8. PrivateWealthManagement
  9. InstitutionalInvestors
  10. TradingEvaluationManagerSelection
    P.S. TradingAdditional
  11. Ethics
    P.S. Ethics_from_Level_II_Code_n_Standards

Two Approaches for Forecasting Exchange Rate

The first approach is that analysts focus on flows of export and imports to establish what the net trade flows are and how large they are relative to the economy and other, potentially larger financing and investment flows. The approach also considers differences between domestic and foreign inflation rates that relate to the concept of purchasing power parity. Under PPP, the expected percentage change in the exchange rate should equal the difference between inflation rates. The approach also considers the sustainability of current account imbalances, reflecting the difference between national saving and investment.

The second approach is that the analysis focuses on capital flows and the degree of capital mobility. It assumes that capital seeks the highest risk-adjusted return. The expected changes in the exchange rate will reflect the differences in the respective countries’ assets’ characteristics such as relative short-term interest rates, term, credit, equity and liquidity premiums. The approach also considers hot money flows and the fact that exchange rates provide an across the board mechanism for adjusting the relative sizes of each country’s portfolio of assets.

Source by CFA reading materials

Dutch Disease

In Dutch Disease, certain sectors have enormous exports demand, which would drive the demand of currency for that country. Its currency appreciates. However, the rest sectors that may not have such huge amount of exports demand would also have to undergo an appreciation of currency. Export demands for goods and services in the rest sectors would decrease even severe.

The Impact of Balance of Payments Flows

As noted earlier, the parity conditions may be appropriate for assessing fair value for currencies over long horizons, but they are of little use as a real-time gauge of value. There have been many attempts to find a better framework for determining a currency’s short-run or long-run equilibrium value. Let’s now examine the influence of trade and capital flows.

A country’s balance of payments consists of its (1) current account as well as its (2) capital and (3) financial account. The official balance of payments accounts make a distinction between the “capital account” and the “financial account” based on the nature of the assets involved. For simplicity, we will use the term “capital account” here to reflect all investment/financing flows. Loosely speaking, the current account reflects flows in the real economy, which refers to that part of the economy engaged in the actual production of goods and services (as opposed to the financial sector). The capital account reflects financial flows. Decisions about trade flows (the current account) and investment/financing flows (the capital account) are typically made by different entities with different perspectives and motivations. Their decisions are brought into alignment by changes in market prices and/or quantities. One of the key prices—perhaps the key price—in this process is the exchange rate.

Countries that import more than they export will have a negative current account balance and are said to have current account deficits. Those with more exports than imports will have a current account surplus. A country’s current account balance must be matched by an equal and opposite balance in the capital account. Thus, countries with current account deficits must attract funds from abroad in order to pay for the imports (i.e., they must have a capital account surplus).

When discussing the effect of the balance of payments components on a country’s exchange rate, one must distinguish between short-term and intermediate-term influences on the one hand and longer-term influences on the other. Over the long term, countries that run persistent current account deficits (net borrowers) often see their currencies depreciate because they finance their acquisition of imports through the continued use of debt. Similarly, countries that run persistent current account surpluses (net lenders) often see their currencies appreciate over time.

However, investment/financing decisions are usually the dominant factor in determining exchange rate movements, at least in the short to intermediate term. There are four main reasons for this:

  • Prices of real goods and services tend to adjust much more slowly than exchange rates and other asset prices.
  • Production of real goods and services takes time, and demand decisions are subject to substantial inertia. In contrast, liquid financial markets allow virtually instantaneous redirection of financial flows.
  • Current spending/production decisions reflect only purchases/sales of current production, while investment/financing decisions reflect not only the financing of current expenditures but also the reallocation of existing portfolios.
  • Expected exchange rate movements can induce very large short-term capital flows. This tends to make the actualexchange rate very sensitive to the currency views held by owners/managers of liquid assets.

Current Account Imbalances and the Determination of Exchange Rates

Current account trends influence the path of exchange rates over time through several mechanisms:

  • The flow supply/demand channel
  • The portfolio balance channel
  • The debt sustainability channel

Let’s briefly discuss each of these mechanisms next.

The Flow Supply/Demand Channel

The flow supply/demand channel is based on a fairly simple model that focuses on the fact that purchases and sales of internationally traded goods and services require the exchange of domestic and foreign currencies in order to arrange payment for those goods and services. For example, if a country sold more goods and services than it purchased (i.e., the country was running a current account surplus), then the demand for its currency should rise, and vice versa. Such shifts in currency demand should exert upward pressure on the value of the surplus nation’s currency and downward pressure on the value of the deficit nation’s currency.

Hence, countries with persistent current account surpluses should see their currencies appreciate over time, and countries with persistent current account deficits should see their currencies depreciate over time. A logical question, then, would be whether such trends can go on indefinitely. At some point, domestic currency strength should contribute to deterioration in the trade competitiveness of the surplus nation, while domestic currency weakness should contribute to an improvement in the trade competitiveness of the deficit nation. Thus, the exchange rate responses to these surpluses and deficits should eventually help eliminate—in the medium to long run—the source of the initial imbalances.

The amount by which exchange rates must adjust to restore current accounts to balanced positions depends on a number of factors:

  • The initial gap between imports and exports
  • The response of import and export prices to changes in the exchange rate
  • The response of import and export demand to changes in import and export prices

If a country imports significantly more than it exports, export growth would need to far outstrip import growth in percentage terms in order to narrow the current account deficit. A large initial deficit may require a substantial depreciation of the currency to bring about a meaningful correction of the trade imbalance.

A depreciation of a deficit country’s currency should result in an increase in import prices in domestic currency terms and a decrease in export prices in foreign currency terms. However, empirical studies often find limited pass-through effects of exchange rate changes on traded goods prices. For example, many studies have found that for every 1% decline in a currency’s value, import prices rise by only 0.5%—and in some cases by even less—because foreign producers tend to lower their profit margins in an effort to preserve market share. In light of the limited pass-through of exchange rate changes into traded goods prices, the exchange rate adjustment required to narrow a trade imbalance may be far larger than would otherwise be the case.

Many studies have found that the response of import and export demand to changes in traded goods prices is often quite sluggish, and as a result, relatively long lags, lasting several years, can occur between (1) the onset of exchange rate changes, (2) the ultimate adjustment in traded goods prices, and (3) the eventual impact of those price changes on import demand, export demand, and the underlying current account imbalance.

The Portfolio Balance Channel

The second mechanism through which current account trends influence exchange rates is the so-called portfolio balance channel. Current account imbalances shift financial wealth from deficit nations to surplus nations. Countries with trade deficits will finance their trade with increased borrowing. This behaviour may lead to shifts in global asset preferences, which in turn could influence the path of exchange rates. For example, nations running large current account surpluses versus the United States might find that their holdings of US dollar–denominated assets exceed the amount they desire to hold in a portfolio context. Actions they might take to reduce their dollar holdings to desired levels could then have a profound negative impact on the dollar’s value.

“Shifts in Global Asset Preferences” means would alter the components of assets allocation in the portfolio.

The Debt Sustainability Channel

The third mechanism through which current account imbalances can affect exchange rates is the so-called debt sustainability channel. According to this mechanism, there should be some upper limit on the ability of countries to run persistently large current account deficits. If a country runs a large and persistent current account deficit over time, eventually it will experience an untenable rise in debt owed to foreign investors. If such investors believe that the deficit country’s external debt is rising to unsustainable levels, they are likely to reason that a major depreciation of the deficit country’s currency will be required at some point to ensure that the current account deficit narrows significantly and that the external debt stabilises at a level deemed sustainable.

The existence of persistent current account imbalances will tend to alter the market’s notion of what exchange rate level represents the true, long-run equilibrium value. For deficit nations, ever-rising net external debt levels as a percentage of GDP should give rise to steady (but not necessarily smooth) downward revisions in market expectations of the currency’s long-run equilibrium value. For surplus countries, ever-rising net external asset levels as a percentage of GDP should give rise to steady upward revisions of the currency’s long-run equilibrium value. Hence, one would expect currency values to move broadly in line with trends in debt and/or asset accumulation.

Reference

CFA Readings

Value at Risk & Expected Shortfalls

Value at Risk – VaR

VaR is a probability statement about the potential change in the value of a portfolio.

Notation

$$Porb(x\leq VaR(X))= 1-c$$

$$ Prob\bigg(z \leq \frac{VaR(X)-\mu}{\sigma}\bigg)=1-c $$

  • $c$ – confidence interval, i.e. $c=99\%$. Then $1-c = 1\% $
  • $\mu$ and $\sigma$ are for $X$.
    • For Example, if X is yearly return, then \mu_{252days}=252\cdot\mu_{1day}, and \sigma_{252days}=\sqrt{252}\cdot\sigma_{1day}
  • $x$ here is the return. So, $c$ is the confidence interval, i.e. 99%.
    • VaR focus on the tail risks. If x stands for return, then tail risk is on the left tail, z_{1-c}.
  • If x is the loss, the tail risk is on the right tail. z_c

$$VaR(X) = \mu + \sigma\cdot \Phi^{-1}(1-c)$$

$$VaR(X) = \mu + \sigma\cdot z_{1-c}$$

  • I.E.

​ If c=99\%, then 1-c=1\%, so z_{1-c}=z_{0.01} \approx -2.33

​ VaR(X) = \mu – 2.33\cdot \sigma

P.S.

​ The unit of VaR is the amount of loss, so it should be monetary amount. For example, if the total amount of portfolio is USD 1 million, then VaR = \$1m \cdot (\mu – 2.33\cdot \sigma).

Loss Distribution

Remember X is a distribution of loss. If we know the distribution of Portfolio Return R, R\sim N(\mu, \sigma^2), then what is the dist for X?

$$X \sim N(-\mu, \sigma^2)$$

Right! Loss is just the negative return. Also, the volatility would not be affected by plus / minus.

Expected Shortfall (ES)

Expected Shortfall states the Expected Loss during time T conditional on the loss being greater than the c^{th} percentile of the loss distribution.

Notation

$$ ES_c (X) = \mathbb{E}\bigg[ X|X\leq VAR_c(X) \bigg] $$

  • Be attention here, X is a r.v., and x stands for return here! while the only variable in the ES_c(X) is c, the confidence level, instead of X.
  • $c$ is the confidence level, i.e. $c$ = 99%.
  • If x stands for return, then the VaR is the left-tail, z_{1-c}.

$$ ES_c (X) = \mathbb{E}\bigg[ X|X\geq VAR_c(X) \bigg] $$

  • If x stands for loss (, which is the negative of return ), then the VaR is the right-tail, z_{c}.

Derivation

Notation Form

Consider, x is the return, then ES_c (X) = \mathbb{E}\bigg[ X|X\leq VAR_c(X) \bigg], and VaR_c(x)= \mu + z_{1-c}\sigma, where c is the confidence level c=99\% for example.

$$ES_c(X) = \frac{\int_{-\infty}^{VaR} xf(x)dx }{\int_{-\infty}^{VaR} f(x)dx } = \frac{\int_{-\infty}^{VaR} x \phi(x)dx }{\int_{-\infty}^{VaR} \phi(x)dx } =\frac{\int_{-\infty}^{VaR} x \phi(x)dx }{ \Phi(VaR) – \Phi(-\infty)} $$

$$= \frac{1}{ \Phi(VaR) – \Phi(-\infty) }\int_{-\infty}^{VaR}x \frac{1}{\sqrt{2\pi \sigma^2}} e^{-\frac{(x-\mu)^2}{2\sigma^2}} dx $$

Replace z = \frac{x-\mu}{\sigma}, then x = \mu + z \sigma, and dx = \sigma dz

$$ = \frac{1}{\Phi(VaR)} \int_{-\infty}^{VaR}(\mu + z\sigma) \frac{1}{\sqrt{2\pi \sigma^2}} e^{-\frac{z^2}{2}}\sigma dz $$

$$ = \frac{1}{\Phi(VaR)}\mu \int_{-\infty}^{VaR}\frac{1}{\sqrt{2\pi }} e^{-\frac{z^2}{2}} dz + \sigma^2\int_{-\infty}^{VaR} z \frac{1}{\sqrt{2\pi \sigma^2}} e^{-\frac{z^2}{2}} dz $$

$$ = \frac{1}{\Phi(VaR)}\mu \Phi(VaR) – \frac{\sigma^2}{\Phi(VaR)}\int_{-\infty}^{VaR} \frac{1}{\sqrt{2\pi \sigma^2}} e^{-\frac{z^2}{2}} d(-\frac{z^2}{2}) $$

$$ = \mu – \frac{\sigma^2}{\Phi(VaR)} \frac{1}{\sqrt{2\pi \sigma^2}} \int_{-\infty}^{VaR} e^{-\frac{z^2}{2}} d(-\frac{z^2}{2}) $$

$$ = \mu – \frac{\sigma}{\Phi(VaR)} \frac{1}{\sqrt{2\pi }} e^{-\frac{z^2}{2}} |_{-\infty}^{VaR} $$

$$ = \mu – \frac{\sigma}{\Phi(VaR)} \frac{1}{\sqrt{2\pi }} e^{-\frac{VaR^2}{2}}= \mu – \frac{\sigma}{\Phi(VaR)} \phi(VaR)$$

Recall, VaR_c(x)= \mu + z_{1-c}\sigma, so \phi(VaR_c(x))= \phi(\mu + z_{1-c}\sigma) \leftrightarrow \phi(z_{1-c}) = \phi\bigg( \Phi^{-1}(1-c) \bigg), and \Phi(VaR_c(x))= \Phi(\mu + z_{1-c}\sigma) \leftrightarrow \phi(z_{1-c}) = \Phi\bigg( \Phi^{-1}(1-c) \bigg) = 1-c.

Thus,

$$ ES_c(X) =\mu – \frac{\sigma}{\Phi(VaR)} \phi(VaR)=\mu -\sigma \frac{\phi\big( \Phi^{-1}(1-c) \big)}{1-c}$$

VaR Form

we ‘sum up’ (integrate) the VaR from c to 1, conditional on 1-c.

$$ES_c(X) = \frac{1}{1-c} \int_c^1 VaR_u(X)du$$

$$ ES_c(X) = \frac{1}{1-c} \int_c^1 \bigg( \mu + \sigma\cdot \Phi^{-1}(1-u) \bigg) du $$

$$ =\mu + \frac{\sigma}{1-c} \int^1_c \Phi^{-1}(1-u) du $$

We let u = \Phi(Z), where Z \sim N(0,1). Then,

  • $du =d(\Phi(z)) =\phi(z) dz$.
  • $u\in (c,1)$, so $z = \Phi^{-1}(u)\in (z_c \ , \infty)$

Thus,

$$ ES_c(X) =\mu + \frac{\sigma}{1-c} \int^{\infty}_{z_c} \Phi^{-1}\big(1-\Phi(z)\big)\phi(z) dz $$

As 1-\Phi(z) = \Phi(-z)

$$ ES_c(X) =\mu + \frac{\sigma}{1-c} \int^{\infty}_{z_c} \Phi^{-1}(\Phi(-z))\phi(z) dz = \mu – \frac{\sigma}{1-c} \int^{\infty}_{z_c} z\phi(z) dz $$

$ \int_{z_c}^{\infty} z \phi(z)dz = \int_{z_c}^{\infty} z \frac{1}{\sqrt{2\pi}}e^{-\frac{z^2}{2}}dz = -\frac{1}{\sqrt{2\pi}} \int_{z_c}^{\infty} -e^{\frac{z^2}{2}}d(e^{-\frac{z^2}{2}})$

$=\frac{1}{\sqrt{2\pi}}e^{-\frac{z_c^2}{2}}=\phi(z_c)=\phi\big(\Phi^{-1}(c)\big)$, bring it back to $ES_c(X)$

$$ES_c(X) = \mu – \sigma\frac{ \phi\big(\Phi^{-1}(c)\big)}{1-c}$$

Morden Portfolio Theory

  • $x$ – vector weights
  • $R$ – vector of all assets’ returns
  • $\mu = \mathbb{E}(R)$ – mean return of all assets
  • $\Sigma = \mathbb{E}\bigg[ (R-\mu)(R-\mu)^T \bigg]$ – var-cov matrix of all assets

So,

  • $\mu_x = x^T \mu$ – becomes a scalar now
  • $\sigma^2 = x^T \Sigma x$ – collapse to be a scalar

Optimisation

  • Maximise Expected Return s.t. volatility constraint.

$$ \max_{x} \mu_x \quad s.t. \quad \sigma_x \leq \sigma^* $$

  • Minimise Volatility s.t. return constraint.

$$ \min_{x} \sigma_x \quad s.t. \quad \mu_x \geq \mu^* $$

Portfolio Risk Measures

By definition, the loss of a portfolio is the negative of return, L(x) = -R(x).

The Loss distribution becomes the same normal distribution with x-axis reversed.

  • Volatility of Loss: \sigma(L(x)) = \sigma_x, the minus does not matter in the s.d.
  • Standard Deviation-based risk measure: =\mathbb{E}(L(x)) + cz_{c}\sigma(L(x)), x-axis is revered, so z_{1-c} for return becomes z_c for loss.
  • VaR: VaR_{\alpha}(x)=inf\bigg{ \mathscr{l}:Prob\big[ L(x)\leq \mathscr{l} \geq\big] \alpha \bigg}
  • Expected Shortfall: ES_{\alpha}(x) = \frac{1}{1-\alpha} \int_{\alpha}^1 VaR_u(x) du. In other form, ES_{\alpha}(x)=\mathbb{E}\bigg( L(x)| L(x)\geq VaR_{\alpha}(x) \bigg)

As R \sim N(\mu, \Sigma),

  • for our portfolio with weights x, mean = \mu, and \sigma_x = \sqrt{x^T \Sigma x}.
  • for the loss, mean = -\mu, and \sigma_x = \sqrt{x^T \Sigma x}.

Black and Scholes, 1973

See A bit Stochastic Calculus .

For,

$$ dS_t = \mu S_t \ dt +\sigma S_t \ dW_t $$

  • In calculating d f(S_t), we would get, (by Taylor Expansion)

$$ df(S_t) = \bigg( \frac{\partial f}{\partial t} + \frac{\partial f}{\partial S_t}\mu S_t +\frac{1}{2}\frac{\partial^2 f}{\partial S_t^2}\sigma^2 S_t^2 \bigg)dt + \frac{\partial f}{\partial S_t}\sigma S_t \ dW_t $$

  • A Special Form of f(\cdot) is f(S) = log(S),

$$ d\ log(S_t) = \bigg( \mu – \frac{1}{2}\sigma^2 \bigg)dt + \sigma \ dW_t $$

We get Y_t = log S_t is the price of a derivative security with respect to S_t and t and then,

$$ dY_t= \bigg( \frac{\partial Y_t}{\partial t} + \frac{\partial Y_t}{\partial S_t}\mu S_t +\frac{1}{2}\frac{\partial^2 Y_t}{\partial S_t^2}\sigma^2 S_t^2 \bigg)dt + \frac{\partial Y_t}{\partial S_t}\sigma S_t \ dW_t $$

Consider a portfolio \Pi is constructed with (1) short one derivative, and (2) long some fraction of stocks, \Delta, such that the portfolio is risk natural. (\Delta = \frac{\partial Y}{\partial S})

$$ \Pi_t = -Y +\Delta \ S_t $$

Differentiate it,

$$ d\Pi_t = -dY_t +\frac{dY}{dS}dS_t $$

Subtitute dY_t and dS_t into the above equation, we would then get the stochastic process of portfolio, by Ito’s Lemma.

$$ d\Pi_t =-\bigg( \frac{\partial Y}{\partial t} + \frac{1}{2}\frac{\partial^2 Y}{\partial S^2} \sigma^2 S_t^2 \bigg) dt $$

The diffusion term dW_t disappears, and that means the portfolio is riskless during the interval dt. Under a no arbitrage assumption, this portfolio can only earn the riskless return, r.

$$ d\Pi_t =r\Pi_t \ dt $$

  • Subtitute d\Pi_t and \Pi_t into, we would get the Partial Differential Equation (PDE) / Black-Scholes equation,

$$ – \bigg( \frac{\partial Y}{\partial t} + \frac{1}{2}\frac{\partial^2 Y}{\partial S^2} \sigma^2 S_t^2 \bigg) dt = r\bigg(- Y_t + \frac{\partial Y}{\partial S}S_t \bigg)dt $$

$$ rY_t = \frac{\partial Y}{\partial t} + \frac{1}{2}\frac{\partial^2 Y}{\partial S^2} \sigma^2 S_t^2 + \frac{\partial Y}{\partial S}S_t $$

Then, we guess (where U(.) is a function of S_t at time t=T),

$$ Y_t = e^{-r(T-t)} U(S_T) $$

For a European call with strike price, K, U(S_T) would be the payoff at maturity,

$$ U(S_T) = max( S – K , 0 ) $$

Finally, through a series of process to find a specific solution of the PDE, we can solve the value of call, (\Phi(\cdot) is the cumulative standard normal distribtion)

$$ c = S_t\Phi(d_1) – K e^{-r (T-t)}\Phi(d_2) $$

with,

$$ d_1 =\frac{ log(S_t/K) + (r-\frac{1}{2}\sigma^2)(T-t)}{\sigma \sqrt{T-t}} $$

$$ d_1 = \sigma \sqrt{T-t} $$

42-2010_HandbookDownload

Why do Banks run?

Assumption

Entrepreneurs borrow from banks to invest in long-term projects. Banks themselves borrow from risk-averse households, who receive endowments every period. Households deposit their initial endowment in banks in return for demandable deposit claims. There is no uncertainty initially about the average quality of a bank’s projects in our model, so the bank’s asset side is not the source of the problem. However, there is uncertainty about household endowments (or equivalently, incomes) over time.

Process

Firstly, households deposit their initial endowments and have an unexpectedly high need to withdraw deposits.

Anticipated prosperity, as well as current adversity, can increase current household demand for consumption goods substantially.

As households withdraw deposits to satisfy consumption needs, banks will have to call in loans to long gestation projects in order to generate the resources to pay them. The real interest rate will rise to equate the household demand for consumption goods and the supply of these goods from terminated projects.

Results

Thus greater consumption demand will lead to higher real rates and more projects being terminated, as well as lower bank net worth. This last effect is because the bank’s loans pay off only in the long run, and thus fall in value as real interest rates rise, while the bank’s liabilities, that is demandable deposits, do not fall in value.

$$Asset = Liability + Equity$$

in the balance sheet, so as to banks. However, the difference is that banks’ assets are loans and liabilities are deposits from households. If the real interest rate increases, which conveys the increase in the discount rate, then the value of assets for banks would decrease (,by the present value of future cash flows). Liability (debts) keeps constant, then the equity of banks is destroyed.

Eventually, if rates rise enough, the bank may have negative net worth and experience runs, which are destructive of value because all manner of projects, including those viable at prevailing interest rates, are terminated.

Solution

How can this tendency towards banking sector fragility be mitigated?

  1. Capital Structure of Banks

One possibility is to alter the structure of banks. Long-term loans’ value is more volatile if the real interest rate fluctuates.

If banks financed themselves with long-term liabilities (in part我国政策行if the bank finances through long-term loans, that means A=D+E, `D is also volatile to the real interest rate changes, and moves in the similar direction as Asset) that fell in value as real interest rates rose, banks would be doubly stable. The bank hedge itself, hedging the assets by bank debts.

Deposits from households do not make banks stable, compared with financing through bank loans, because deposits could be withdrawn.

The authors stated that competition that banks strive for efficiency determines the capital structure of banks. I personally do not understand that idea, so I will leave it here.

P.S.

Diamond and Rajan (2001) 中指出，银行，作为金融中介，的功能是有human capital能量化或者保证depositors withdraw时 borrower能提供足够的liquidity还给lender (depositor)的问题。

  • 2. Government Intervention

The government may have to intervene to pull the economy or consumption back into place. A typical way of doing so is through lower the interest rate.

The paper states that, reducing interest rates drastically when the financial sector is in trouble, but not raising them quickly as the sector recovers could create incentives for banks to seek out more illiquidity than good for the system. Such incentives may have to be offset by raising rates in normal times more than strictly warranted by macroeconomic conditions.

Put differently, reduce in interest rates could encourage banks to increase leverage or fund even more illiquid projects up front. This could make all parties worse off.

Reference

Diamond, D. and Rajan, R. (2009) (w15197) Illiquidity and Interest Rate Policy. Cambridge, MA: National Bureau of Economic Research DOI: 10.3386/w15197.

Diamond and Rajan’s Study about Financial Crisis 2008

The authors noted the financial crisis of 2008 was caused by mainly three reasons.

  1. U.S. financial sectors misallocated resources to real estate.
  2. Commercial and Investment banks had a large proportion of their instruments in their Balance Sheet.
  3. Investments were largely financed with short-term debts.

The following will illustrate why those facts happen.

1. Misallocation of Investment

Step 1. World Crisis pushed up risks.

The financial crisis in emerging markets, East Asia Econ Collapsed, `Russia Defaulted, South America, etc made investors circumspect.

Step 2. Capital Controls made CA surplus.

To react to those unexpected events and prevent domestic industries from the incumbents, governments started to conduct capital controls. Also, investors were unwilling to invest (they cut down investments and even consumptions) or charge a high-level risk premium. A number of countries became net exporters.

Step 3. “dot-com” bubble derived another global crisis.

Those exporters then had a current accounts surplus and transferred the CA surplus into “savings” (investment). Those savings were invested into the high-return business, the IT industry. However, another nightmare happened that is the “dot-com” bubble collapsed around the 2000s.

Step 4. CB QE and US financial innovations made a housing bubble

Central Banks QE, lowered the interest rate, which ignited demand for housing. The house price spiked. In the U.S., financial innovation (securitization) drew more marginal-credit-quality buyers into the market. The crisis manifested itself.

Step 5. Asymmetric information enforced the bubble.

Because rating agencies were at a distance from the homeowner, they could process only hard information. Asymmetric information enforced the bubble. Housing prices surged to prevent “default”.

Step 6. Securitization Iterate itself.

The slicing and dicing through repeated securitization of the original package of mortgages created very complicated securities. The problems in valuing these securities were not obvious when house prices were rising and defaults were few.

But as the house prices stopped rising and defaults started increasing, the valuation of these securities became very complicated.

2. Why Did Bank hold those instruments?

The key answer is bankers thought those securities were worthwhile investments, despite their risks. Risks were vague and unable to be evaluated.

it is very hard, especially in the case of new products, to tell whether a financial manager is generating true excess returns adjusting for risk, or whether the current returns are simply compensation for a risk that has not yet shown itself but that will eventually materialize.

Several facts manifested the problem.

  • 1. Incentive at the Top

CEOs’ performance is evaluated based in part on the earnings they generate relative to their peers. Peer Pressure, which came from holding financial instruments to increase returns, mutually increased the willingness to hold those financial instruments.

  • 2. Flawed Internal Compensation and Control

The top management wants to maximise the long-term bank value and goals. However, many compensation schemes are paid for short-term risk-adjusted performance. The divergency gave managers an incentive to take risks in the short term.

It is not said that the Risk management team is unaware of such incentives. However, they may be unable to fully control them, because tail risks, by the nature, are hard to quantify before they occur.

  • 3. Short-term Debt

Given the complexity of bank risk-taking, and the potential breakdown in internal control processes, investors would have demanded a very high premium for financing the bank long term. By contrast, they would have been far more willing to hold short-term claims on the bank, since that would give them the option to exit — or get a higher premium — if the bank appeared to be getting into trouble.

In good times, short-term debt seems relatively cheap compared to long-term capital and the costs of illiquidity remote. Markets seem to favor a bank capital structure that is heavy on short-term leverage. In bad times, though, the costs of illiquidity seem to be more salient, while risk-averse (and burnt) bankers are unlikely to take on excessive risk. The markets then encourage a capital structure that is heavy on capital.

  • 4. The Crisis Unfolds

Housing Price decreased, => MBS fall in value and becaome hard to price. Balance sheet destorted, and debt level held, and equity shrinked.

Every parties sold out, drived price down again and again.

Panic (no confidence) spreaded worldwide.

Interbank lendings were forzen as inadequate credits.

  • 5. The `Credit Crunch

Banks were reluctant to lend due to two reasons. One possibility is that they worry about borrower credit risks. A second is that they may worry about having enough liquidity of their own, if their creditor demands funds.

  • Dealing with the Crunch

Banks still fear threats from illiquidity. Illiquid assets still compose significant portions of banks and non-banl balance sheets. The price of those illiquid assets fluctuated largely, because liquidty asset could be easily exchanged or sold out for cash, but illiquid assets were unable to do so so that price shrinked and damaged the balance sheet. Debts held constant, but assets shrinked, resulting in shrinkage of equity, and increase in leverage and financial burden.

Coins have two sides. Low prices mean not only insolvent, but also tremendous buying opportunity. The pandic manified the expectation of insolvency, plus illiquid market condition made the fact that less money was availab to buy at the price. Selling iterated itself.

CB standed out, provided liquidty to financial institutes.

However, an interesting thing happened. CB’s intervention to lend against all manner of collateral may not be a unmitigated bless, because it may allow weak entities to continue holding illiquid assets.

Possible ways to reduce the overhand

1. Authorities offer to buy illiquid assets through auctions. `This can reverse a freeze in the market caused by distressed entities. Fair value from the aution can be higher than the prevailing market price. 2. government ensures the stability of financial system that holds illiquid assets through the recapitalization of entities that have a realistic possibility of survival. （我国，纳入国有）.

Reference

Diamond, Douglas W. and Rajan, Raghuram G., The Credit Crisis: Conjectures About Causes and Remedies (February 2009). NBER Working Paper No. w14739, Available at SSRN: https://ssrn.com/abstract=1347262

A Great Introduction to the Nobel Prize Econ 2022

Here below is a great article introducing the Nobel Prize in Econ in 2022.

A-Great-Article-about-Nobel-Econ-2022-1Download

Later, I will start a series of studies about the journal articles from those Nobel Prize winners. Hopefully, that would help us understand the current crisis.

Reference

Bernanke, B., Gertler, M. and Gilchrist, S. The Financial Accelerator in a Quantitative Business Cycle Framework.

Diamond, D.W. and Dybvig, P.H. ‘Bank Runs, Deposit Insurance, and Liquidity’. JOURNAL OF POLITICAL ECONOMY, p. 19.