# Tag Info

12

The first metric to look at is house-price-to-rent ratios. Rental prices capture the value of the housing (and housing-linked) services provided by a property, including things like how safe a neighborhood is, how good the schools are, et cetera. In contrast, house prices are the capitalized value of the future stream of housing services PLUS the price of an ...

11

This is only a quick answer, unfortunately. The key intuitive insight for Epstein-Zin is that they separate two distinct properties of preferences: risk aversion ("I'd prefer less uncertainty to more uncertainty*") and intertemporal substitution ("I may want to shift consumption forward or backwards in time**"). In the very popular Constant Relative Risk ...

10

I think CompEcon covered most of the points that I was going to mention. Just a few last thoughts: 1) Why are Epstein-Zin preferences important? The preferences are important because they allow you to separate two of the dimensions along which people care about their allocations; namely, risk aversion and intertemporal substitution. Additionally, one ...

9

The name for the amount $56.25 is certainty equivalent. The expected utility for the individual from taking the bet is calculated as follows: $$E[U]=\frac12U(100+125)+\frac12U(100-100)=75$$ Suppose the individual can pay an amount of money$x$so that she can avoid taking the bet (which leads to expected utility$75$). What's the maximum amount of money$x$... 9 It depends on the context, of course, but most often in policy analysis "the value of a life" has nothing (directly) to do with output, etc, but instead means the maximum amount that people would want the government to spend in order to save a randomly chosen life. So in a country of 300,000,000, the question is: What, to you, is the monetary equivalent ... 8 To understand why$\alpha$must be constrained in$(0,1)$, one has to contemplate the meaning of the expression $$\alpha L$$ when$L$is a "lottery". How is a lottery denoted mathematically? Authors do not agree on that: for example, the way Jahle and Reny define a lottery (a "gamble" in their terminology), a lottery can be written as a vector whose ... 8 The answer to 2. is no. One way to see this is from MWG's Property 6.D.2:$F$SOSD$G$if and only if $$\int_0^xF(t)\mathrm dt \le \int_0^xG(t)\mathrm dt \quad\text{for all }x.$$ Dixit calls the two integrals super-cumulative functions of$F$and$G$, respectively. Hence, a characterization of SOSD is that the super-cumulative of ... 7 While it is possible to rigorously define a bubble in principle (see for example asset markets where prices violate transversality conditions), in practice it can be difficult or impossible to identify actual bubbles, even ex-post. For example, @dismalscience discusses looking at house-price-to-rent ratios. This sounds straightforward. If houses are ... 7 Note: I did not vote down on this question, and it is not clear why anyone would do so. Why is so common to suggest university students to specialize in order to get a better paid job? Because the industry evolves and encounters increasingly harder, diverse challenges. Specialized knowledge is essential for coping with those challenges. At the same ... 7 The answer to 1. Your conjecture is correct. Consider lotteries$A,B$where$A$guarantues a payoff of 1 while$B$yields 0 or 4, each with 50% probability.$B$does not SOSD$A$, as you can easily find an agent risk averse enough that they will prefer$A$, e.g. an agent whose preferences are described by$u(x) = \ln(x)$.$A$does not SOSD$B$either, as$E(...

6

You provide a generally correct impression of history (i.e., there were lots of runs on banks by depositors in the US until federal deposit insurance was established— a good history is provided by Gorton (2012)), and then ask three questions: why isn't deposit insurance provided through the private sector, is it because the free market equilibrium premiums ...

6

Handing out the principal amount of debt gradually, in increments, is standard practice in investment loans extended by a bank to a corporation. The rationale is clear : the corporation wants to make an investment, say a new factory. The whole plan is laid out and the cash flows of the pre-operational, construction period are also detailed, based on ...

5

With apologies for the somewhat journalistic answer (as others have noted, even defining a bubble in a rigorous fashion is difficult). Information on housing supply may be of some use. Demand for housing is quite inelastic (everyone needs somewhere to live) so shifts in supply should show up mostly in prices and less in market quantities. As an example, ...

5

This is perhaps a good opportunity to point out that the "certainty equivalence" concept means one thing in microeconomics/choice under uncertainty theory, while it means something different in macroeconomics. Microeconomics/choice under uncertainty The Certainty Equivalent of a lottery/gamble, is the amount of wealth which, if given with certainty, ...

5

Here are a few reasons that build on @Dismalscience's answer. Capital requirements: Banks don't typically need to hold capital against loans they originated but subsequently moved into an SPV. This might be regulatory arbitrage but it might be a socially efficient outcome meant to move assets and liabilities out of the banking system. Market segmentation: ...

5

The seminal academic criticism of dollar cost averaging on many specifications of economic conditions is A Note on the Suboptimality of Dollar-Cost Averaging as an Investment Policy (Constantinides (1979)). You might also be interested in these papers: Dollar Cost Averaging is an investment system that is widely advocated by brokerage firms and mutual ...

5

Suppose that the vector $W=\left(w_1,w_2,\dots,w_n\right)$ represents wealth in $n$ possible states. In addition, assume the probability of each state occurring is represented by the vector $\pi=\left(\pi_1,\pi_2,\dots,\pi_n\right)$. We can express this as the simple gamble: $$g = \left(\pi_1\circ w_1,\pi_2\circ w_2, \dots, \pi_n\circ w_n\right)$$ The ...

4

@Alecos's answer is great. For pedagogical purposes, I'm just going to rephrase some of the steps. We want to show that $ARA = -u''(c)/u'(c)$ given that ARA is defined such that $u(c - ARA/2) = E[u(c + \varepsilon) \mid c]$. So, following Alecos' answer, take a 2nd-order Taylor expansion to get E[u(c + \varepsilon)\mid c] \approx u(c) + \...

4

Set $y \equiv c+\varepsilon$. So $y$ represents changed consumption around and "close" to a given level $c$. Take a 2nd-order Taylor expansion of the function $E[u(y)\mid c]$ around $c$, which is treated as fixed since we condition on it : $$E[u(y)\mid c] \approx E[u(c)\mid c] + E[u'(c)(y-c)\mid c] + E[\frac12u''(c)(y-c)^2\mid c]$$ But $y-c = \varepsilon$ ...

4

Since we are suspecting a corner-solution, it is better to write the problem explicitly with its constraint. Even better, use the Fritz John (FJ) conditions rather than the Karush-Kuhn-Tucker (KKT) ones. We will mention the differences as we go along. $$\max_{\alpha} \int u[w+\alpha(z-1)] dF(z),\;\; \text{s.t.}\;\; w-\alpha \geq 0$$ The lagrangean under ...

4

A variance is an incomplete measure of risk in a sense, that it measures uncertainty in security payoffs, rather than uncertainty in holder's welfare. In the simplest way we can demonstrate this point as follows. Suppose that agents want to marginally increase her holding of an asset by $\xi$ and a unit of asset provides a payoff of $x$, which is a random ...

4

There is a typo in the figure that introduces some confusion in the previous answer, which is basically wrong. Based on the numbers and the figure, the utility is such that $$u=\sqrt{x},$$ so $$E[u]=\frac{1}{2} u(100+125) + \frac{1}{2} u(100−100)= \frac{1}{2} u(225) =\frac{1}{2} \sqrt{225} = 7.5$$. By definition, the risk premium (R) must satisfy the ...

4

It's actually quite easy. The key things to know are 1) that the majority of house purchases are made via mortgage lending, and that 2) an excess of bank lending over bank loan repayment causes money creation. So first determine if there is an abnormally high increase in the supply of money occurring - if yes, then there is a bubble, and if not, then the ...

4

There are two ways I can think of interpreting this question. My first thought is that a single bank doesn't lend out more money than it has, but the banking system does. So let's say someone deposits 100 dollars in Bank A and the reserve requirement is 10%. Then Bank A can lend out 90 dollars. Let's say that money is deposited in Bank B eventually. That ...

4

SPVs are typically used in MBS issuance to get the loans off the issuing bank's balance sheet, freeing up that balance sheet space to make more loans and providing bankruptcy-remoteness (i.e., the SPV would continue to function even if the issuer went bankrupt) to investors. This is why a securitizing bank would transfer loans to an SPV. However, given ...

4

Knight's 1921 essay was not written in formal mathematics (and trying to formulate a direct translation into modern mathematics may be quite problematic). Since Knight's time, a formal decision theory literature has developed which makes distinctions that are at least reminiscent of Knight's. Lars P. Hansen (2012), writes "Motivated by the insights of ...

3

Regarding your first question, the space on which you can apply Lebesgue's theorem is $\mathbb{R}_{+}^{N}$. The relevant $\sigma$-algebra is the Borel $\sigma$-algebra and the integration corresponds to the Lebesgue measure. Formally, with your notation, the function $f_m$ is defined on vectors $x=(x_1,\cdots,x_N)$ by \begin{equation*} f_m(x_1,\cdots,x_N) = ...

3

For alternative measurements of risk, consider: 1. Maximum Adverse Excursion [MAE]- the largest historical loss suffered by a system, trade or investment whether real or back-test. 2. Average True Range [ATR] a measure of price change capturing high/low/close and gaps: http://stockcharts.com/school/doku.phpd=chart_school:technical_indicators:...

3

I'll direct you to wikipedia which has some pretty good information about it. One of the important things about speculative bubbles is that they are very difficult to identify before they burst. It is very difficult to say the market is overvaluing an asset or a change in economic conditions have raised the true value. That said, there are some signs that a ...

3

Given a utility function $u(c)$, $c>0$, with $u'(c)>0, u''(c) <0$. Regarding the sign of the second derivative, if it is zero, then both measures are zero, if it is positive, it would imply increasing marginal utility, and I don't remember having seen these attitude-towards-risk measures for such a utility function. Denote Absolute Risk Aversion (...

Only top voted, non community-wiki answers of a minimum length are eligible