Optimal asset allocation during retirement in the presence of fixed and variable immediate life annuities (payout annuities)

A system for allocating portfolio assets of an investor among annuity and nonannuity vehicles, comprising:

• a memory for storing at least one probability of survival of the investor, at least one of a utility of consumption attributed to the investor and a utility of bequest attributed to the investor, data identifying a plurality of nonannuity assets having different rates of return and degrees of risk, data identifying a plurality of annuity assets having different rates of return and degrees of risk;
• a processor coupled to the memory to retrieve the stored probability of survival, the stored utility of bequest or utility of consumption and said data identifying the annuity and nonannuity assets, the processor maximizing an objective utility function as the sum of a utility of a live state and a utility of a dead state given the retrieved rates of return by adjusting the values of a plurality of investment weighting factors, each factor being a weight of a respective nonannuity or annuity asset;
• and
• a portfolio asset allocator coupled to an output of the processor for allocating assets in the portfolio responsive to the adjusted values of the investment weighting factors which result in a maximum of the objective utility function.

A system for optimally allocating investment assets for a given user within and between annuitized assets and non-annuitized assets, comprising:

• a computer having a CPU and memory;
• means for providing to the computer at least one of the user's utility of consumption and utility of bequest;
• means for providing to the computer the user's objective probability of survival based on the user's age;
• means for providing to the computer the user's subjective probability of survival based on the user's physical well-being;
• means for providing to the computer an expected rate of return from each of a plurality of assets, ones of the assets being riskier than others of the assets;
• and
• means for maximizing an objective utility function which is calculated as a function of the asset expected rates of return, a utility of a live state of the user and a utility of a dead state of the user and a plurality of asset allocation weights respectively corresponding to the different assets.

A machine-readable medium on which has been prerecorded a computer program which, when executed by a processor, performs the following steps:

• retrieving at least one probability of survival of an investor;
• selecting a utility of consumption and a utility of bequest of the investor;
• retrieving, for each of a plurality of annuity assets and nonannuity assets, an expected rate of return, each nonannuity asset and each annuity asset having an expected rate of return and a degree of risk which is different from others of the assets;
• maximizing an objective utility function as the sum of a utility of a live. state and a utility of a dead state given the retrieved rates of return by adjusting the values of a plurality of investment weighting factors corresponding to respective ones of the annuity and nonannuity assets;
• and
• allocating wealth in a portfolio of the investor comprising the nonannuity assets and the annuity assets according to the investment weighting factors for which the objective utility function is maximized.

A method for allocating assets of an investor to a plurality of annuity and ponannuity investment vehicles, comprising the steps of:

• retrieving personal characteristics of the investor, the characteristics including age, a risk aversion measure and at least one of a utility of consumption and a utility of bequest;
• retrieving data about the financial wealth of the investor, including, for each investment vehicle presently employed by the investor, a measure of risk of the investment vehicle, a rate of expected return for the investment vehicle, and an amount of wealth in the investment vehicle, the sum of the wealth in the investment vehicles being the total financial wealth of the investor;
• classifying the investment vehicles of the investor into allocatable investment vehicles whose assets may be reallocated, and nonallocatable investment vehicles whose assets may not be reallocated;
• providing a plurality of asset classes having varying degrees of risk and expected return, the asset classes including nonannuity asset classes and annuity asset classes;
• attributing the present investment vehicles of the investor to the asset classes as a function of the risk and expected return of the asset class and the investment vehicle;
• maximizing an objective utility function as the sum of a utility of a live state and a utility of a dead state given the rates of expected return of the asset classes by adjusting values of a plurality of investment weighting factors each corresponding to an asset class;
• and
• rebalancing the total financial wealth of the investor among the asset classes as a function of the investment weighting factors by adjusting the amount of assets held in each of the allocatable investment vehicles.

A method of comparing a current allocation of assets in an investment portfolio by a portfolio manager with an optimum allocation of the wealth of the portfolio among a plurality of annuity and nonannuity assets, comprising the steps of:

• retrieving, for the investor for which the portfolio has been established, at least one probability of survival;
• retrieving for the investor a utility of consumption and a utility of bequest;
• retrieving, for each of the annuity and nonannuity assets, an expected rate of return, ones of the annuity assets having rates of return which are different from others of the annuity assets, ones of the nonannuity assets having rates of return which are different from others of the nonannuity assets;
• relating a utility of a live state of the investor to a utility of a dead state of the investor as a function of the utility of consumption and the utility of bequest;
• maximizing an objective utility function as the sum of the utility of the live state and the utility of the dead state given the retrieved rates of return by adjusting the values of a plurality of investment weighting factors each corresponding to one of the annuity assets or one of the nonannuity assets;
• making a proposed allocation of the wealth of the portfolio among the nonannuity assets and the annuity assets according to the relative values of the investment weighting factors;
• comparing the proposed allocation to the current allocation;
• and
• modifying the current allocation in view of the proposed allocation.