Let's just be clear here: Leave the diamonds at home. Don't bring anything with you that you'd hate to lose. If you do bring any valuables with you, leave them in the hotel safe when you go out. The same goes for important documents, such as your passport and travel visas.
Don't carry more than small amounts of cash. Instead, use traveler's checks or a credit card -- both are traceable and replaceable if you lose them. Pickpockets are rampant, so carry your money in different places on your body, rather than together in a highly visible fanny pack. For example, put your credit card in your jacket pocket and your cash in your front pants pocket. If you do wear a money belt, place it under your shirt or jacket so that it's not visible. Women who want to carry a purse should choose one with a thick strap and wear it across the chest.
Bring your credit card numbers and the phone number of your credit card company with you and put them in the hotel safe when you go out. That way, if your credit card is stolen, you can report it right away and put a freeze on the card so the thief can't use it.
Keep your belongings close to you at all times. When you put your suitcase on the curb in front of the hotel, don't wander away from it -- keep your eye on it at all times.
Stay away from anyone who attempts to part you from your money, including scam artists who offer you items at "bargain prices" or who approach you on the street and offer to give you a local tour. Be wary if someone bumps into you or tries to otherwise distract you (such as by asking you for the time) -- the person might be a pickpocket.