I have $2M in retirement savings. I am trying to decide among the following retirement options.

a. Purchasing an annuity from an insurance company.

b. Investing in a managed bond mutual fund that only buys high grade bonds. I would live off the interest payments and/or sell bonds as needed to live.

please provide me some information and pros and cons on each of the above options.

An annuity from an insurance company would be a better retirement option. 

Annuity is a contractual agreement that binds the insurance company to make payments during annuitization and the annuity holder to make regular payments towards the fund to earn an income stream in future.

 Advantages of Retirement Annuities

• Guaranteed returns
• Deferred Taxation
• Life-Long Income Flow

Disadvantages of Retirement Annuities

• High front end costs
• Higher taxation
• Complex structure and mechanism
• Sequestration of liquidity

Bond Mutual Fund: Specialized mutual fund engaging capital in the High-grade Bond based investment opportunities.

Advantages of Bond Mutual Fund/High-grade Bond funds.

• Preservation of capital
• Stable income based on interest and increased NAV 
• Capital Gain Distribution.

Disadvantages of Bond Mutual Fund/High-grade Bond funds.

• Low levels of return
• Volatility in NAV based bonds' market value 
• Management fee and related charges

Step-by-step explanation

Annuity as a Retirement option

Annuities (Retirement Annuities) is the most promising investment  based on its inherent advantage of providing guaranteed and consistent flow of income for the life of the retiree/annuity holder. Retirement Annuities funded in prior years for the futures income flow, as a closed and static form of regular/lump sum payments provide lower levels of liquidity. 

• Several forms of retirement annuities available in the insurance marketplace, such as Fixed Annuities similar to a Certificate of Deposit for which the payment made by the insurance company is predetermined on the basis of a fixed rate of return. 
• Immediate Annuities involves a lump sum payment followed by immediate regular payments. 
• Whereas Variable Annuities are linked to the performance of subaccounts (collection of stocks and/or bonds) in the financial market.
• Deferred Annuities locks in the payment stream for a particular duration before the beginning of annuitization can be associated with the advantages of fixed or variable annuities.

Advantages of Retirement Annuities

• For the fixed type of annuities a consistent rate of return is assured, as the predetermined rate of return helps in planning and forecasting retirement income streams.
• Taxation of annuities is an advantage point for annuity holders as the incidence of tax occurs at maturity with withdrawal of funds. 
• It forms the basis of social security by providing income flow that lasts till death.

Disadvantages of Retirement Annuities

• As compared with other investment opportunities such as mutual funds, high sales commission is associated with annuities charged by the agent and even the insurance companies charge direct cost in practice, resulting in higher investment entry load. 
• As the deferred taxation advantage of annuities comes with the related  disadvantage of  high taxation on interest earned / value appreciation more than capital gain tax and tax charged equivalent to the ordinary income based on the tax bracket of the retiree. 
• As the insurance industry matured over the last decades, the complexity of structured products comes with the dense variability on contractual terms documents, incomprehensible for retiree in general, makes the return uncertain in the absolute terms, such as equity-indexed linked annuities.
• High penalties and restrictions are attached with the withdrawal from annuity funds, makes it less liquid than other investment alternatives.

High-grade Bond funds as a Retirement option:

Mutual funds under this category invest in the investment-grade bonds, entitled with high rating provided by credit rating agencies, associated with minimized risk of default consequently lower levels of returns.

Advantages of High-grade Bond funds

• Predictable semi-annually interest (in general) related distribution of income.
• Repayment of capital based prevailing NAV price results in capital preservation.
• Comparatively less volatile than other categories mutual funds such as blue-chip /equity based funds. 
• Consistent Distribution of capital based profits by the fund to the unit holders.
• Stability in the NAV price levels and growth based marketability 
• Professionally managed the fund capital protects the capital against the unpredictable market moves.

Disadvantages of High-grade Bond funds

• NAV of the fund as related to the underlying bonds can decrease by the fall in the price of the bonds in the market.
• High levels of management related fee and charges result in low levels of return as compared to holding individual bonds.
• As the fund is constantly engaged in the bond market, future performance is comparatively less predictable than annuities.
• Directly linked with market volatility of the underlying class of the bond.

Therefore, analyzing the requirement of retirement and the comparison of investment opportunities available based on the factors like stability, income stream and security retirement annuities are the superior choice over the other retirement investment such as Bond Mutual Funds/ High-grade Bond funds.