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A portfolio that gives maximum return for a given risk, or minimum risk for given return is an efficient portfolio. Thus, portfolios are selected as follows: (a) From the portfolios that have the same return, the investor will prefer the portfolio with lower risk, and [ 1 ]
For example, for bond options [3] the underlying is a bond, but the source of uncertainty is the annualized interest rate (i.e. the short rate). Here, for each randomly generated yield curve we observe a different resultant bond price on the option's exercise date; this bond price is then the input for the determination of the option's payoff.
Merton's portfolio problem is a problem in continuous-time finance and in particular intertemporal portfolio choice.An investor must choose how much to consume and must allocate their wealth between stocks and a risk-free asset so as to maximize expected utility.
An example of the former would be choosing the proportions placed in equities versus bonds, while an example of the latter would be choosing the proportions of the stock sub-portfolio placed in stocks X, Y, and Z. Equities and bonds have fundamentally different financial characteristics and have different systematic risk and hence can be viewed ...
In contrast, modern portfolio theory is based on a different axiom, called variance aversion, [27] and may recommend to invest into Y on the basis that it has lower variance. Maccheroni et al. [ 28 ] described choice theory which is the closest possible to the modern portfolio theory, while satisfying monotonicity axiom.
A conditional variance swap is a type of variance swap or swap derivative product that allows investors to take exposure to volatility in the price of an underlying security but only while the underlying security is within a pre-specified price range.
to be a variance strike and L {\displaystyle L} be a notional amount converting the payoffs into a unit amount of money, say, e.g., USD or GBP, then payoffs at expiry for the call and put options written on R V d {\displaystyle RV_{d}} (or just variance call and put) are
Payoff chart from buying a butterfly spread. Profit from a long butterfly spread position. The spread is created by buying a call with a relatively low strike (x 1), buying a call with a relatively high strike (x 3), and shorting two calls with a strike in between (x 2).