Investment Beahvioral Finance

Sharpe ratio depicts the risk premium of an asset or portfolio in relation to the total risk

Treynor ratio depicts the risk premium in relation to the systematic risk Beta

utility is increasing with wealth at a decreasing rate:

u’(x) > 0 Mehr Reichtum mehr Nutzen

u’’(x) < 0 Nutzenwahrnehmung nimmt mit zunehmendem Gewinn ab

Variance refers to the spread of a data set around its mean value, and so it measures the risk of an asset/portfolio. 

Covariance refers to the measure of the directional relationship between two random variables.

A positive covariance means both investments' returns tend to move upward or downward in value at the same time. An inverse or negative covariance, on the other hand, means the returns will move away from each other.

covariance talks about the direction – positive or negative – of the relationship between two variables.

correlation talks about the direction, as well as, the strength of the relationship between the variables.

\(f' = {1\over\ x}\)

\(f' = {1\over\ x}\)

\(f' = {3\over\ x}\)

\( = {-sin(x)}\)

\(f'(x) = {cosx}\)

VaR systematic = RP x Qstd x Var(Index) x Beta

Technicians seek to project the level at which a financial instrument will trade, whereas fundamental analysts seek to predict where it should trade.

Convexity measures how the interest rate sensitivity of a financial instrument changes with the level of rates. It contributes to price changes when rates start to move.

• Convexity is a measure of the curvature in the relationship between bond prices and bond yields.
• Convexity demonstrates how the duration of a bond changes as the interest rate changes.
• If a bond's duration increases as yields increase, the bond is said to have negative convexity.
• If a bond's duration rises and yields fall, the bond is said to have positive convexity.

• Conservatism
• Aversion to ambiguity
• Confirmation
• Representativenes
• Illusion of control
• Hindsight
• Disjunction

• Anchoring
• Mental accounting
• Framing
• Overreaction
• magical thinking
• sunk cost
• forecasting error
• overreaction and availability 

• Loss aversion
• Overconfidence
• Self control
• Status Quo
• Endowment
• Regret aversion
• Naive Diversification

• Gambler's Fallacy
• Herd behaviour

People tend to overweight the base rates and underweight the new information, resulting in revised beliefs about probabilities and outcomes that demonstrate an under-reaction to the new information.

• Many people become anchored to their ideas and will not update their expectations when new information arrives (anchoring bias)
• Only tentative and insufficient reaction to news
• This underreaction to news leads to momentum in stock returns (initial under-reaction).

People prefer the familiar to the unfamiliar.

An investment manager with deeper knowledge and experiences in bonds prefers the certainty of bond cash flows to the uncertainty of risk asset cash flows, even though investors might receive appropriately higher returns for assuming that risk.

People give more weight to evidence that (1) supports their beliefs and (2) ignore or modify evidence that conflicts with their beliefs.

“Human Ratio” behind it:

• faulty reasoning - easily corrected
• feelings - harder to correct

People classify new information based on past experiences and classifications. Judgements based on stereotypes.

• People tend to overestimate the representativeness of single observations and small samples

• May result in overreaction and correction anomalies, e.g. reversal in prices

• People judge by similarity to familiar types, without regard to base rate probabilities.

• Tendency to see patterns in what is really random walk
  – TechnicalAnalysis,e.g.randompatternsareusedforforecasting

People tend to believe that they can control or influence outcomes when, in fact, they can not.

Believe in technical analysis and trading signals or patterns.

People may see past events as having been predictable and reasonable to expect.

- Very similar to illusion of control bias.

Errors in information processing leads to: 

• misestimate of probabilities of

− Probable events.
− The probability of events. 

− Future risks and returns.

When required to estimate a value with unknown magnitude, people generally begin by envisioning some initial default number—an “anchor”—which they then adjust up or down to reflect subsequent information and analysis. People place undue weight on the anchor.

Note: The “anchor” still works even if it’s not related to the actual problem at all!

People treat one sum of money differently from another equal-sized sum based on which mental account the money is assigned to.

Examples:

• Treatment of real estates
• Handling of wins on the stock market: “lets take more bets – is funny money anyway ...”
• Spending money you won in a lottery or you had to earn.

Framing bias occurs when people make a decision based on the way the information is presented

Framing for Minimal
People consider only differences between local options. Example: Gaining $5, disregarding common features.

Comprehensive Framing
People consider something in relation to one other. Example: A customer might include both camera and calculator in relation to something else, for instance total monthly expenses

Topical Framing

People considers the context in which the decision arises. Example: The process of reducing the price of the calculator from $15 to $10. People usually frame decisions in terms of topical accounts.

Example: The savings on the calculators are considered relative to their prices in each option

According to the availability bias, people tend to heavily weight their decisions toward more recent information, making any new opinion biased toward that latest news.

People base decisions on available information and resonation information, which they weight.

Those information can have several sources: It can be caused by retrievability, categorization, a narrow range of experiences, and resonance.

People take a heuristic (mental shortcut) approach to estimating the probability of an outcome. Sometimes they measure it based on how easily the outcome comes to their mind.

• People tend to weight too much recent experience compared to prior beliefs – so called memory bias (also: exponential weighting in time series analysis).

• Analysts tend to excessively extrapolate historical trends when forecasting future earnings/cash flows - extrapolation bias.

Skinner Example:
B. F. Skinner 1948, fed hungry pigeons mechanically at 15-second intervals.

Pigeons developed superstitions

Peoples reactions to stock market events follow also patterns. These responses have similar origins.

• People bet more on coin not yet tossed.

• People pay more for lottery ticket in which they choose the

  number

• ... a bit like Illusion of Control Bias

Example 1: Playing with a tennis elbow in a tennis club, in spite of pain. This maintains the evaluation of the membership fee as a cost rather than a sunk loss.

Example 2: Continuing a project that has already cost a lot without any results, rather than starting a new one, although the previous costs are sunk costs.

Example 3:

People tend to eat bad-tasting food just because they have already paid for.

Framing negative outcomes as costs rather than as a loss improves subjective feelings